全色数与小阶路的混合Ramsey数

The Mixed Ramsey Numbers: Total Chromatic Number Versus Small Paths

以χ２（Ｇ）记一图Ｇ之全色数，Ｐｎ表ｎ阶路，混合Ｒａｍｓｅｙ数χ２（ｍ，Ｐｎ）为最小正整数ｐ，对于每个ｐ阶图Ｇ，或者χ２（Ｇ）≥ｍ，或者ＧＰｎ。当ｍ取任意正整数、ｎ≤４时，本文得到χ２（ｍ。

Let the total chromatic number of a graph G be denoted by χ 2(G) , the path of order n by P n . The mixed Ramsey number χ 2(m,P n) is the least positive integer p so that for any graph G of order p , either χ 2(G)≥m or the complement contains P n as a subgraph. We has detemined the mixed Ramsey numbers χ 2(m,P n) for every m and n≤4 .