Pith. sign in

REVIEW 3 major objections 3 minor 1 cited by

Tight Hamilton Cycles in Linearly Quasirandom 3-Graphs

T0 review · 3 major / 3 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read For a 3-graph of density p > 1/3, minimum codegree above δ0(p)n forces a tight Hamilton cycle, and this bound is sharp; the earlier 1/4 conjecture fails at p0 ≈ 0.318.

desk verdict A real advance that likely settles the p>1/3 threshold and disproves the 1/4 conjecture, but the parameter hierarchy in the connecting lemma is not closed and one core regularity lemma is only sketched. read the letter →

arxiv 2607.21568 v1 pith:IUQULKMI submitted 2026-07-23 math.CO

Xichao Shu This is my paper · ORCID
classification math.CO MSC 05C6505C4505D40
keywords tightHamiltoncycles3-uniformhypergraphsquasirandomminimumcodegreeregularsliceabsorptionmethodpair-stategraphscalarlemma
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper settles, for densities above 1/3, how much common-neighbour structure a quasirandom 3-uniform hypergraph must have to be guaranteed to contain a tight Hamilton cycle — a cyclic ordering in which every three consecutive vertices form an edge. It first disproves the natural conjecture that density and minimum codegree both above 1/4 suffice: a balanced split of the vertex set into two parts of sizes x0n and p0n (where x0^3 + x0 = 1, p0 = x0^3 ≈ 0.318) yields a (p0−ε, μ)-dense 3-graph with minimum codegree at (p0−ε)n and no tight Hamilton cycle. For every p > 1/3 the paper then determines the exact asymptotic threshold: if minimum codegree exceeds δ0(p)n = ((1−√((4p−1)/3))/2)^2 n, a tight Hamilton cycle is forced, and a biased version of the earlier construction shows no smaller codegree bound can work. The proof reduces the problem to a finite system of scalar inequalities and shows that above the threshold only the trivial solutions exist, so a directed 'pair-state' graph is strongly connected and aperiodic, enabling fixed-length connecting paths.

What carries the argument

The proof rests on a regular slice that partitions every ordered pair of vertices into a bounded number of 'pair-cells', each with bounded relative weight. Dense regular triads of pair-cells define transitions in a directed pair-state graph whose vertices are the pair-cells; a walk in this graph tracks the terminal ordered pair of a growing tight path. The central reduced statement is that this digraph is strongly connected and aperiodic when p > 1/3 and α > δ0(p). To prove this, a non-trivial closed set of states is shown to produce a weight matrix (s_ij) satisfying the scalar inequalities Φ(s_ij, s_jk, s_ki) ≥ τ and Σ_k λ_k s_jk s_ki ≥ Δ (plus a mirrored inequality for 1−s), and a convexit

What would settle it

A numerical search could look for a non-trivial matrix (s_ij) ∈ [0,1]^{I×I} and weights (λ_i) summing to one satisfying the three scalar inequalities of Lemma 5.4 for some τ > 1/3 with Δ > a(τ)^2 (where a(τ) is the smaller root of a^3 + (1−a)^3 = τ); finding one would falsify the scalar lemma and hence the connecting argument. Alternatively, exhibiting, for some p > 1/3 and ε > 0, a (p, μ)-dense 3-graph on arbitrarily large vertex sets with δ2 ≥ (δ0(p)+ε)n and no tight Hamilton cycle would falsify Theorem 1.3 directly.

Watch

Extended reading notes

Core claim

The central claim is that the map p ↦ δ0(p) = ((1−√((4p−1)/3))/2)^2 is the asymptotically sharp minimum-codegree threshold for tight Hamilton cycles in (p, μ)-dense 3-graphs whenever p > 1/3: every sufficiently large such n-vertex 3-graph with δ2(H) ≥ αn for α > δ0(p) contains a tight Hamilton cycle, while for every ε > 0 there are (p, μ)-dense 3-graphs with δ2 ≥ (δ0(p)−ε)n and no tight Hamilton cycle. A second claim is that the previously proposed p, α > 1/4 condition is false; the number p0 = max_{0≤x≤1} min{x^3, 1−x} ≈ 0.317672 supplies a counterexample that is both (p0−ε, μ)-dense and has minimum codegree at least (p0−ε)n yet lacks a tight Hamilton cycle because of a global imbalance bet

Load-bearing premise

The proof assumes the hypergraph can be sliced into pair-cells so that every needed triad is regular and every positive density survives the splitting of clusters into subclusters; this 'regular slice with local cleaning' step is cited as a standard consequence of the hypergraph regularity lemma rather than proved in detail, and if it fails the reduced pair-state digraph and the entire connecting argument collapse.

Editorial extensions

If this is right

  • The conjectured condition p, α > 1/4 does not force tight Hamilton cycles; the honest threshold only exists for p > 1/3.
  • For every p > 1/3, δ0(p)n is the asymptotically sharp minimum-codegree threshold, so the answer to the problem of the full threshold function h(p) is now known on that whole range.
  • The arbitrary-pair connecting method cannot be pushed below p = 1/3: even minimum codegree slightly above n/3 does not guarantee that every two ordered pairs can be joined by a tight path once density drops below 1/3.
  • Any sharp Hamiltonicity result for p ≤ 1/3 will need to control the endpoints of absorbers and path covers within a selected family of connectable pairs, since a global connecting lemma fails there.
  • The full threshold function h(p) for 0 < p ≤ 1/3 is left open; for the diagonal value p_diag (the first p with h(p) ≤ p), the two theorems bracket p0 ≤ p_diag ≤ 1/3, and the paper asks whether in fact p_diag = p0.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The balanced constant p0 arises from equating two competing obstructions (x^3 and 1−x); analogous 'balancing constants' may appear in the threshold functions for tight Hamilton cycles in k-uniform quasirandom hypergraphs under other minimum-degree conditions, a pattern worth testing numerically.
  • The pair-state digraph plus scalar-lemma template is a general recipe: it reduces a global spanning problem to a finite convexity statement, and the same template could plausibly be adapted to tight paths of fixed length or to loose Hamilton cycles in quasirandom hypergraphs.
  • The threshold function h(p) may have a genuine phase transition at or near p0, since the two constructions presented give different extremal mechanisms on different sides of p0; deciding whether h(p) drops sharply to the right of p0 would clarify the structure of extremal quasirandom 3-graphs.
  • One concrete testable extension is to check numerically whether the scalar obstruction at Δ = a(τ)^2 from Remark 5.5 is the only obstruction for τ slightly above 1/3, which would indicate whether the connecting lemma is tight exactly at the stated boundary.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper studies tight Hamilton cycles in 3-graphs that are linearly quasirandom in the sense of (p,μ)-density, under a minimum codegree condition. It first constructs, for p0≈0.317672, (p0−ε,μ)-dense 3-graphs with minimum codegree at least (p0−ε)n and no tight Hamilton cycle, disproving a conjecture of Araújo, Piga and Schacht (Problem 1.1). It then proves for every p>1/3 that the sharp asymptotic minimum-codegree threshold is δ0(p)=((1−√((4p−1)/3))/2)^2: every sufficiently large (p,μ)-dense 3-graph H with δ2(H)≥αn, α>δ0(p), contains a tight Hamilton cycle, and a biased construction shows the bound is best possible. The positive theorem is deduced from the absorption framework of Han–Shu–Wang via a fixed-length connecting lemma. The connecting lemma is proved through a regular slice, a directed pair-state graph whose states are ordered pair-cells, a finite scalar lemma ruling out non-trivial closed sets, and a lifting argument from reduced walks to tight paths. The paper also gives a construction showing that below p=1/3, minimum codegree slightly above n/3 does not force arbitrary ordered pairs to be connectable.

Significance. If the proof of the connecting lemma is made fully rigorous, the results constitute a substantial advance: they solve the sharp minimum-codegree threshold for tight Hamilton cycles in linearly quasirandom 3-graphs for all p>1/3, give an explicit counterexample to a natural conjecture, and identify p=1/3 as a genuine boundary for the arbitrary-pair connecting method. The constructions in Section 2 are explicit, self-contained, and correct; the scalar lemma (Lemma 5.4) is elegant and its proof is convincing. The paper is honest about the limitations of the method below p=1/3. However, the central proof currently rests on a regularity claim (Lemma 4.3) and a repeated-cluster convention that are only sketched, and the parameter hierarchy linking the size of the regular slice to the length of the reduced walks appears circular as written. These issues are load-bearing and require substantial clarification before the main theorem can be considered established.

major comments (3)
  1. [§5, proof of Lemma 1.4; §4.2, Lemma 4.3] The quantifier order in the proof of Lemma 1.4 is circular. Lemma 4.3 takes δ2, δ3, and a regularity parameter r as inputs and returns M0; then L=L(M0) is defined via Lemma 5.2, and t=L+2 becomes the pattern size in Lemma 5.3. Lemma 5.3 applies Lemma 4.2 with pattern size L+2, and Lemma 4.2 requires δ2, δ3 to be very small and the triad-regularity parameter to be at least some function of L. Since L is not known until M0 is produced, the stated order — first choose "all regularity parameters sufficiently small", then define M and L — does not guarantee that the slice is regular enough for the extension lemma. A rigorous hierarchy must be supplied, e.g. by proving a version of Lemma 4.3 that explicitly bounds M0 in terms of the input parameters and then choosing parameters by a fixed-point argument, or by an iterative refinement argument. As written, the reduced walk may be too long for t
  2. [§4.2, Lemma 4.3] Property (3) of Lemma 4.3 is genuinely stronger than the global irregularity bound in the standard regular-slice lemma of [3], because it asserts a local bound over every pair-cell of weight at least 1/M0. The proof sketch ('ε(t) ≪ η t^{-C}') does not quantify C, nor how the returned M0 interacts with the pair-cell weight lower bound, nor how the bounded refinements for reversal coherence affect the local estimates. Since Lemma 4.5 (reduced codegree inheritance) relies precisely on property (3) to feed the reduced extension inequalities and hence the scalar lemma, this lemma is load-bearing and must be proved in full or replaced by a precisely stated reference.
  3. [§4.2, repeated-cluster convention; used in §5.3, Lemma 5.3] The repeated-cluster convention asserts that splitting clusters into subclusters preserves all regularities and positive densities, with losses 'absorbed into the parameter hierarchy'. This is used essentially in Lemma 4.4 and in Lemma 5.3 when a reduced walk revisits clusters many times. In Lemma 5.3, the walk length r=L can be a growing function of M0, so a single cluster may be used O(L) times. The number of required subclusters and the resulting degradation of δ2, δ3 (and of the positive densities of pair-cells and dense triads) are not quantified. Without this quantification, the application of Lemma 4.2 in Lemma 5.3 is not fully justified.
minor comments (3)
  1. [§4.3, Lemma 4.4(2)] The displayed identity for the total reduced weight of a subfamily of triads is stated as an equality. When two or three indices coincide, the product of pair-cell weights counts ordered triples with repeated vertices, whereas the support K3(T) excludes them. The identity is therefore only true up to o(1), and the statement should say so to avoid a formal gap.
  2. [§1.2 / Theorem 1.2] The conclusion that the constructed H is (p0−ε, μ)-dense uses the definition's additive error μ n^3, not a relative error. This is correct, but the argument would be clearer if the definition of (p,μ)-density were explicitly recalled at that point, since for very small subsets X,Y,Z the error term dominates.
  3. [§3, Theorem 3.1] The absorption framework of [20] is used as a black box, and [20] is by the same authors. The theorem is stated in full, which is helpful; a sentence on where the theorem is proved or published would aid readers in verifying that the stated hypotheses (in particular the reservoir condition) match the published result.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the sharp threshold is proved by an independent scalar lemma and matched by explicit constructions; the self-citations are framework citations, not forced inputs.

full rationale

The central claims do not reduce to their own inputs by construction. Theorem 1.3's threshold delta_0(p) is not fitted: it is the inverse of the density/codegree curve of the biased Araujo-Piga-Schacht lower-bound construction, while the positive direction is proven by the reduced scalar lemma (Lemma 5.4), a self-contained finite inequality that rules out non-trivial closed sets in the pair-state digraph. The lower-bound constructions (Constructions 1, 2, 3) are explicit and checked directly via the quasirandom two-colouring lemma; the no-Hamilton-cycle arguments are independent of the positive threshold. The absorption framework [20, Theorem 1.9] is a load-bearing self-citation, but it is a general sufficient condition whose stated assumptions do not include the target threshold, so it is independent support rather than a circular premise. Lemma 4.3 is only sketched as a standard consequence of [3], and the repeated-cluster convention of Section 4.2 is asserted rather than proved; these are technical gaps in rigor, and the M0/L parameter-order concern is a possible constant-hierarchy issue, not a derivation of the conclusion from an equivalent input. None of these steps exhibit Eq. X = Eq. Y by construction or a fitted parameter renamed as a prediction. The paper's own limitations and proof sketches are flagged here but do not amount to circularity.

Assumptions & free parameters 2 free parameters · 8 assumptions · 0 invented entities

The central claims rest on the (p,μ)-density definition, a standard regularity slice (cited), counting/extension lemmas, the absorption framework from the author's own earlier work, and the paper's repeated-cluster slicing convention. The two construction parameters (x0, ρ) are extremal-example parameters, not fitted predictions. No new postulates, particles, or forces are introduced; the pair-state digraph and scalar-lemma inequalities are proof devices, not independent entities.

free parameters (2)
  • x0 (Construction 1 balance point) = x0 ≈ 0.6823278 (unique root of x^3 + x = 1)
    Defines p0 = 1 − x0 = x0^3 ≈ 0.317672. Chosen to maximize min{x^3, 1−x}; it is the balancing point of two density constraints in the counterexample, not a value fitted to the theorem's conclusion.
  • ρ (biased sharpness construction parameter) = ρ ∈ (0,1/2]; for each p > 1/3, the smaller root of ρ^3 + (1−ρ)^3 = p
    Parameter of Construction 2; the codegree lower bound is ρ^2 n, and inverting the curve q(ρ) = p yields δ0(p). This parameter is free in the extremal example rather than fitted to a prediction.
assumptions (8)
  • domain assumption Definition of (p, μ)-density: e_H(X,Y,Z) ≥ p|X||Y||Z| − μn^3 for all subsets X,Y,Z (Definition 1)
    The entire problem is posed in this one-sided quasirandomness framework; all theorems are conditional on this definition.
  • standard math Existence of quasirandom red–blue colourings of complete graphs with prescribed pair/triangle densities (Lemma 2.1)
    Proved in the paper via independent random colourings and concentration bounds; used in all three constructions.
  • standard math Hypergraph regular-slice lemma of Allen–Böttcher–Cooley–Mycroft [3], error-function version, plus bounded cleaning (Lemma 4.3)
    Cited as a black box; produces the ordered pair-cell partitions and the local cleaning properties used to define the pair-state digraph. The paper gives only a sketch of the derivation.
  • standard math Dense counting lemma and extension lemma for regular complexes ([11, Lemmas 5 and 6])
    Used in Lemmas 4.4, 4.5 and 5.3 to turn reduced weights into edge counts and to extend endpoint copies to full tight paths.
  • standard math Absorption framework: connectability plus reservoir condition forces a Hamilton cycle ([20, Theorem 1.9])
    Black box from the author's own prior work; the proof of Theorem 1.3 reduces to verifying the connecting and reservoir conditions.
  • standard math Reservoir lemma for minimum codegree ([24, Lemma 8.1])
    Used in Section 3 to select the random reservoir A with the required codegree concentration.
  • standard math Fixed-length walks in strongly connected aperiodic directed graphs (Lemma 5.2, [29])
    Converts strong connectivity plus aperiodicity of the pair-state digraph into walks of one common length L.
  • ad hoc to paper Repeated-cluster splitting convention preserves all regularities and positive densities (Section 4.2)
    Assumed so that bounded patterns reusing a cluster (e.g., (Vi,Vi,Vi)) can be embedded with the same regular slice; the slicing/refinement details are not provided.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Tight Hamilton Cycles in Linearly Quasirandom 3-Graphs." pith.science (2026). https://pith.science/paper/IUQULKMI

@misc{pith2026260721568,
  author       = {Pith},
  title        = {Pith review of: Tight Hamilton Cycles in Linearly Quasirandom 3-Graphs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IUQULKMI}},
  note         = {Machine review of arXiv:2607.21568}
}
abstract

We study tight Hamilton cycles in linearly quasirandom 3-graphs. An $n$-vertex 3-graph $H$ is $(p,\mu)$-dense if $e_H(X,Y,Z)\ge p|X||Y||Z|-\mu n^3$ for all $X,Y,Z\subseteq V(H)$. Ara{\'u}jo, Piga and Schacht asked whether $p,\alpha>1/4$ together with $\delta_2(H)\ge\alpha n$ force a tight Hamilton cycle. We give a negative answer: for every $\varepsilon,\mu>0$ and all sufficiently large $n$, there exists an $n$-vertex $(p_0-\varepsilon,\mu)$-dense 3-graph $H$ with $\delta_2(H)\ge(p_0-\varepsilon)n$ and no tight Hamilton cycle, where $p_0:=\max_{0\le x\le1}\min\{x^3,1-x\}\approx0.317672$. For every $p>1/3$, we determine the asymptotically sharp minimum-codegree threshold. Writing \[ \delta_0(p)= \left(\frac{1-\sqrt{(4p-1)/3}}{2}\right)^2, \] we prove that every sufficiently large $(p,\mu)$-dense 3-graph $H$ with $\delta_2(H)\ge\alpha n$ contains a tight Hamilton cycle whenever $\alpha>\delta_0(p)$ and $\mu$ is sufficiently small. A matching construction shows that this threshold is best possible. The proof uses absorption together with a new fixed-length connecting lemma based on a regular slice, a directed pair-state graph, and a finite scalar lemma.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sharp Diagonal Thresholds for Tight Hamilton Cycles in Uniformly Dense $3$-Graphs

    math.CO 2026-07 accept novelty 7.0 of 10

    For linearly quasirandom 3-graphs, tight Hamilton cycles are forced by vertex-degree above the curve f(d) when d>1/3, while the sharp codegree diagonal is κ≈0.3177, not 1/4.

Reference graph

Works this paper leans on

36 extracted references · cited by 1 Pith paper

  1. [3]

    Allen, J

    P. Allen, J. B¨ ottcher, O. Cooley, and R. Mycroft. Tight cycles and regular slices in dense hypergraphs.Journal of Combinatorial Theory, Series A, 149:30–100, 2017

    2017

  2. [20]

    J. Han, X. Shu, and G. Wang. Non-linear hamilton cycles in linear quasirandom and uniformly dense hypergraphs.Journal of Combinatorial Theory, Series B, 177:1–30, 2026

    2026

  3. [1]

    Aigner-Horev, D

    E. Aigner-Horev, D. Conlon, H. H` an, Y. Person, and M. Schacht. Quasirandomness in hyper- graphs.Electronic Journal of Combinatorics, 25(3):Paper No. 3.34, 2018

    2018

  4. [2]

    Aigner-Horev and G

    E. Aigner-Horev and G. Levy. Tight hamilton cycles in cherry-quasirandom 3-uniform hyper- graphs.Combinatorics, Probability and Computing, 30(3):412–443, 2021

    2021

  5. [4]

    Ara´ ujo, S

    P. Ara´ ujo, S. Piga, and M. Schacht. Localised codegree conditions for tight hamilton cycles in 3-uniform hypergraphs.SIAM Journal on Discrete Mathematics, 36(1):147–169, 2022

    2022

  6. [5]

    Buci´ c, J

    M. Buci´ c, J. W. Cooper, D. Kr´ al’, S. Mohr, and D. Munh´ a Correia. Uniform Tur´ an density of cycles.Transactions of the American Mathematical Society, 376(7):4765–4809, 2023

    2023

  7. [6]

    F. R. K. Chung. Quasi-random classes of hypergraphs.Random Structures & Algorithms, 1(4):363–382, 1990

    1990

  8. [7]

    F. R. K. Chung. Regularity lemmas for hypergraphs and quasi-randomness.Random Structures & Algorithms, 2(2):241–252, 1991

    1991

Show all 36 references
  1. [8]

    F. R. K. Chung. Quasi-random hypergraphs revisited.Random Structures & Algorithms, 40(1):39–48, 2012

    2012

  2. [9]

    F. R. K. Chung, R. L. Graham, and R. M. Wilson. Quasi-random graphs.Combinatorica, 9(4):345–362, 1989

    1989

  3. [10]

    Conlon, H

    D. Conlon, H. H` an, Y. Person, and M. Schacht. Weak quasi-randomness for uniform hyper- graphs.Random Structures & Algorithms, 40(1):1–38, 2012

    2012

  4. [11]

    Cooley, N

    O. Cooley, N. Fountoulakis, D. K¨ uhn, and D. Osthus. Embeddings and Ramsey numbers of sparsek-uniform hypergraphs.Combinatorica, 29:263–297, 2009

    2009

  5. [12]

    G. A. Dirac. Some theorems on abstract graphs.Proceedings of the London Mathematical Society, 2(1):69–81, 1952

    1952

  6. [13]

    P. Erd˝ os. On the combinatorial problems which i would most like to see solved.Combinatorica, 1(1):25–42, 1981

    1981

  7. [14]

    Erd˝ os and V

    P. Erd˝ os and V. T. S´ os. On Ramsey-Tur´ an type theorems for hypergraphs.Combinatorica, 2(3):289–295, 1982. 23

    1982

  8. [15]

    Erd˝ os and A

    P. Erd˝ os and A. H. Stone. On the structure of linear graphs.Bulletin of the American Mathematical Society, 52:1087–1091, 1946

    1946

  9. [16]

    Gan and J

    L. Gan and J. Han. Hamiltonicity in cherry-quasirandom 3-graphs.European Journal of Combinatorics, 99:103457, 2022

    2022

  10. [17]

    Garbe, D

    F. Garbe, D. Kr´ al’, and A. Lamaison. Hypergraphs with minimum positive uniform Tur´ an density.Israel Journal of Mathematics, 259:701–726, 2024

    2024

  11. [18]

    Glebov, D

    R. Glebov, D. Kr´ al’, and J. Volec. A problem of erd˝ os and s´ os on 3-graphs.Israel Journal of Mathematics, 211:349–366, 2016

    2016

  12. [19]

    J. Han, X. Shu, and G. Wang. Non-linear hamilton cycles in linear quasi-random hypergraphs. InProceedings of the 2021 ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 594–608. SIAM, 2021

    2021

  13. [21]

    G. Y. Katona and H. A. Kierstead. Hamiltonian chains in hypergraphs.Journal of Graph Theory, 30(3):205–212, 1999

    1999

  14. [22]

    P. Keevash. Hypergraph Tur´ an problems. In R. Chapman, editor,Surveys in Combinatorics 2011, volume 392 ofLondon Mathematical Society Lecture Note Series, pages 83–140. Cam- bridge University Press, 2011

    2011

  15. [23]

    Kohayakawa, B

    Y. Kohayakawa, B. Nagle, V. R¨ odl, and M. Schacht. Weak hypergraph regularity and linear hypergraphs.Journal of Combinatorial Theory, Series B, 100(2):151–160, 2010

    2010

  16. [24]

    K¨ uhn, R

    D. K¨ uhn, R. Mycroft, and D. Osthus. Hamiltonℓ-cycles in uniform hypergraphs.Journal of Combinatorial Theory, Series A, 117(7):910–927, 2010

    2010

  17. [25]

    Lenz and D

    J. Lenz and D. Mubayi. Eigenvalues and linear quasirandom hypergraphs.Forum of Mathe- matics, Sigma, 3:e2, 2015

    2015

  18. [26]

    Lenz and D

    J. Lenz and D. Mubayi. The poset of hypergraph quasirandomness.Random Structures & Algorithms, 46(4):762–800, 2015

    2015

  19. [27]

    J. Lenz, D. Mubayi, and R. Mycroft. Hamilton cycles in quasirandom hypergraphs.Random Structures & Algorithms, 49(2):363–378, 2016

    2016

  20. [28]

    W. Mantel. Problem 28.Wiskundige Opgaven, 10:60–61, 1907

    1907

  21. [29]

    S. W. Neufeld. A diameter bound on the exponent of a primitive directed graph.Linear Algebra and its Applications, 245:27–47, 1996

    1996

  22. [30]

    C. Reiher. Extremal problems in uniformly dense hypergraphs.European Journal of Combi- natorics, 88:103117, 2020

    2020

  23. [31]

    Reiher, V

    C. Reiher, V. R¨ odl, A. Ruci´ nski, M. Schacht, and E. Szemer´ edi. Minimum vertex degree condition for tight hamiltonian cycles in 3-uniform hypergraphs.Proceedings of the London Mathematical Society, 119(2):409–439, 2019. 24

    2019

  24. [32]

    Reiher, V

    C. Reiher, V. R¨ odl, and M. Schacht. Hypergraphs with vanishing Tur´ an density in uniformly dense hypergraphs.Journal of the London Mathematical Society, 97(1):77–97, 2018

    2018

  25. [33]

    Reiher, V

    C. Reiher, V. R¨ odl, and M. Schacht. On a Tur´ an problem in weakly quasirandom 3-uniform hypergraphs.Journal of the European Mathematical Society, 20(5):1139–1159, 2018

    2018

  26. [34]

    R¨ odl, A

    V. R¨ odl, A. Ruci´ nski, and E. Szemer´ edi. An approximate Dirac-type theorem fork-uniform hypergraphs.Combinatorica, 28(2):229–260, 2008

    2008

  27. [35]

    Towsner.σ-algebras for quasirandom hypergraphs.Random Structures & Algorithms, 50(1):114–139, 2017

    H. Towsner.σ-algebras for quasirandom hypergraphs.Random Structures & Algorithms, 50(1):114–139, 2017

    2017

  28. [36]

    P. Tur´ an. On an extremal problem in graph theory.Matematikai ´ es Fizikai Lapok, 48:436–452, 1941. 25

    1941

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.