中文

无偶圈图的边数上界

组合数学 2019-08-16 v4

摘要

我们证明,对于每个固定的 kk,一个不包含长度为 2k2k 的圈的 nn 顶点图,其边数至多为 80klogkn1+1/k+O(n)80\sqrt{k}\log k\cdot n^{1+1/k}+O(n)

关键词

引用

@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}
}

备注

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