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Long induced paths in expanders

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Nemanja Draganić, Peter Keevash

Combinatorics · Submitted 3 Feb 2024

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length.

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arXiv ID2402.02256 (version 2)
Pith ID4JXASLTR, Pith's permanent record of this paper and its review
CitationNemanja Dragani\'c, Peter Keevash. "Long induced paths in expanders." arXiv:2402.02256 (2024). https://pith.science/paper/4JXASLTR
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The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,886 input tokens.

What the abstract itself states, as probabilities: claims first 0.89 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.02 · states quantitative result 0.31 · compares with prior results 0.95 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, strengthening an analogous result in the random setting by Dragani\'c, Glock and Krivelevich. More generally, we find long induced paths in sparse graphs that satisfy a mild upper-uniformity edge-distribution condition.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. result 0.94 0.97 0.94 asserted 1.00
s1 This is the first such result for expanders, strengthening an analogous result in the random setting by Dragani\'c, Glock and Krivelevich. contribution 0.36 0.52 0.09 asserted 1.00
s2 More generally, we find long induced paths in sparse graphs that satisfy a mild upper-uniformity edge-distribution condition. result 0.77 0.95 0.12 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

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not examined
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  • figures and tables
  • references and citing sentences
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We prove that any bounded degree regular graph with sufficiently strong spectral expansion contains an induced path of linear length. This is the first such result for expanders, strengthening an analogous result in the random setting by Dragani\'c, Glock and Krivelevich. More generally, we find long induced paths in sparse graphs that satisfy a mild upper-uniformity edge-distribution condition.

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1 arXiv paper cite this in 1 sentence

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites

Cites as background 3 papers
  • For more background we refer the reader to the survey [ref] and recent papers [ref] .

    2207.05048 · Induced size-Ramsey number of paths · 1.00

  • For more background we refer the reader to the survey [ref] and recent papers [ref] .

    Effective bounds for induced size-Ramsey numbers of cycles · Induced size-Ramsey number of paths · 1.00

  • For example, the Snake-in-the-box Problem [ref] , motivated by the theory of error-correcting codes [ref] , asks for the longest induced path in the hypercube graph.

    Combinatorial Gray codes-an updated survey · Introduction · 0.91

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