Extremal numbers for cycles in a hypercube

Maria Axenovich

Extremal numbers for cycles in a hypercube

Combinatorics 2022-11-29 v2

Authors: Maria Axenovich

Abstract

Let $ex(Q_n, H)$ be the largest number of edges in a subgraph $G$ of a hypercube $Q_n$ such that there is no subgraph of $G$ isomorphic to $H$ . We show that for any integer $k\geq 3$ , $ex(Q_n, C_{4k+2})= O(n^{\frac{5}{6} + \frac{1}{3(2k-2)}} 2^n).$

Keywords

graph cycles hypergraph theory cubic fourfolds

Cite

@article{arxiv.2211.12842,
  title  = {Extremal numbers for cycles in a hypercube},
  author = {Maria Axenovich},
  journal= {arXiv preprint arXiv:2211.12842},
  year   = {2022}
}

Comments

New reference [18] for a better bound by I.Tomon is added

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