English

A bound on the number of edges in graphs without an even cycle

Combinatorics 2019-08-16 v4

Abstract

We show that, for each fixed kk, an nn-vertex graph not containing a cycle of length 2k2k has at most 80klogkn1+1/k+O(n)80\sqrt{k}\log k\cdot n^{1+1/k}+O(n) edges.

Keywords

Cite

@article{arxiv.1403.1601,
  title  = {A bound on the number of edges in graphs without an even cycle},
  author = {Boris Bukh and Zilin Jiang},
  journal= {arXiv preprint arXiv:1403.1601},
  year   = {2019}
}

Comments

16 pages, v2 appeared in Comb. Probab. Comp., v3 fixes an error in v2 and explains why the method in the paper cannot improve the power of k further, v4 fixes the proof of Theorem 12 introduced in v3