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Improved bounds for the extremal number of subdivisions

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arxiv 1809.00468 v1 pith:DFJGSAWA submitted 2018-09-03 math.CO

Oliver Janzer This is my paper · ORCID
classification math.CO
keywords constantexiststextthereboundsconlonextremalfrac
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abstract

Let $H_t$ be the subdivision of $K_t$. Very recently, Conlon and Lee have proved that for any integer $t\geq 3$, there exists a constant $C$ such that $\text{ex}(n,H_t)\leq Cn^{3/2-1/6^t}$. In this paper, we prove that there exists a constant $C'$ such that $\text{ex}(n,H_t)\leq C'n^{3/2-\frac{1}{4t-6}}$.

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Cited by 2 Pith papers

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

  1. A note on pseudorandom Ramsey graphs

    math.CO 2019-09 conditional novelty 7.0 of 10

    For fixed s, optimal K_s-free pseudorandom graphs would imply r(s,t)=t^{s-1+o(1)}, and new constructions improve the cycle Ramsey lower bounds to r(C5,t) > t^{11/8} and r(C7,t) > t^{11/9}.

  2. Bipartite Tur\'an problems for ordered graphs

    math.CO 2019-08 accept novelty 7.0 of 10

    For t by t split patterns, the new upper bound is n^{2 - 1/t + o(1)}, and for one-sided t-split patterns it is n^{2 - 1/t + 1/(2t^2) + o(1)}.

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