您当前的位置: > 详细浏览

A LOWER BOUND OF THE NUMBER OF EDGES IN A GRAPH CONTAINING NO TWO CYCLES OF THE SAME LENGTH

请选择邀稿期刊:
摘要: In 1975, P. Erd {o}s proposed the problem of determining the maximum number $f(n)$ of edges in a graph of $n$ vertices in which any two cycles are of different  lengths. In this paper, it is proved that $$f(n) geq n+32t-1$$ for $t=27720r+169 , (r geq 1)$  and $n geq frac{6911}{16}t^{2}+ frac{514441}{8}t- frac{3309665}{16}$. Consequently, $ liminf sb {n to infty} {f(n)-n over sqrt n} geq sqrt {2 + {2562 over 6911}}.$

版本历史

[V2] 2024-03-26 18:31:45 ChinaXiv:202205.00103V2 下载全文
[V1] 2022-05-14 19:48:27 ChinaXiv:202205.00103v1 查看此版本 下载全文
点击下载全文
预览
同行评议状态
通过
许可声明
metrics指标
  •  点击量8713
  •  下载量656
评论
分享