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Some open problems on cycles

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摘要: Let f(n) be the maximum number of edges in a graph on n vertices in which no two cycles have the same length. Erd¨os raised the problem of determining f(n). Erd¨os conjectured that there exists a positive constant c such that ex(n, C2k) ≥ cn1+1/k. Haj´os conjecture that every simple even graph on n vertices can be decomposed into at most n/2 cycles. We present the problems, conjectures related to these problems and we summarize the know results. We do not think Haj´os conjecture is true.

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[V3] 2024-03-27 19:52:21 ChinaXiv:202210.00147V3 下载全文
[V1] 2022-10-22 10:43:34 ChinaXiv:202210.00147v1 查看此版本 下载全文
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