Multicolour Ramsey numbers of paths and even cycles
Multicolour Ramsey numbers of paths and even cycles
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DOI：
10.1016/j.ejc.2017.03.002
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发表时间：
2016-06
期刊：
影响因子：
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通讯作者：
Ewan Davies;Matthew Jenssen;Barnaby Roberts
中科院分区：
文献类型：
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作者：
Ewan Davies;Matthew Jenssen;Barnaby Roberts
We prove new upper bounds on the multicolour Ramsey numbers of paths and even cycles. It is well known that (k− 1) n+ o (n)⩽ R k (P n)⩽ R k (C n)⩽ k n+ o (n). The upper bound was recently improved by Sárközy who showed that R k (C n)⩽ k− k 16 k 3+ 1 n+ o (n). Here we show R k (C n)⩽(k− 1 4) n+ o (n), obtaining the first improvement to the coefficient of the linear term by an absolute constant.
