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arXiv 1902.02646math.CO
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大$n$的所有Ramsey $(C_n,K_6)$临界图

All Ramsey $(C_n,K_6)$ critical graphs for large $n$

Chula J. Jayawardene, W. Chandanie W. Navaratna, J. N. Senadheera

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14 pages, 4 figures
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摘要：

设$G$和$H$是有限图。如果对于一个完全图$K_n$的边的任何两个着色，有一个$G$的第一个颜色（红色）的副本，或者有一个$H$的第二个颜色（蓝色）的副本，我们称之为$K_n\rightarrow (G,H)$。拉姆齐数$r(G, H)$定义为最小正整数$n$，使得$K_{n} \rightarrow (G, H)$。$K_{r(G, H)-1}$的一个双着色使得$K_{r(G, H)-1} \not \rightarrow (G,H)$称为临界着色。Ramsey临界$r(G, H)$图是由临界着色的第一颜色诱导的图。本文证明了当$n \geq 15$时，恰好存在68个非同构的Ramsey临界$r(C_n, K_6)$图.

英文摘要：

Let $G$ and $H$ be finite graphs. If for any two-coloring of the edges of a complete graph $K_n$, there is a copy of $G$ in the first color, red, or a copy of $H$ in the second color, blue, we will say $K_n\rightarrow (G,H)$. The Ramsey number $r(G, H)$ is defined as the smallest positive integer $n$ such that $K_{n} \rightarrow (G, H)$. A two-coloring of $K_{r(G, H)-1}$ such that $K_{r(G, H)-1} \not \rightarrow (G,H)$ is called a critical coloring. A Ramsey critical $r(G, H)$ graph is a graph induced by the first color of a critical coloring. In this paper, when $n \geq 15$, we show that there exist exactly sixty eight non-isomorphic Ramsey critical $r(C_n, K_6)$ graphs.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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