论文信息 - Some three-color Ramsey numbers, R(P4, P5, Ck) and R(P4, P6, Ck)

Some three-color Ramsey numbers, R(P4, P5, Ck) and R(P4, P6, Ck)

For given graphs G"1,G"2,G"3, the three-color Ramsey number R(G"1,G"2,G"3) is defined to be the least positive integer n such that every 3-coloring of the edges of complete graph K"n contains a monochromatic copy of G"i colored with i, for some [email protected][email protected]?3. In this paper, we prove that R(P"4,P"5,C"3)=11, R(P"4,P"5,C"4)=7, R(P"4,P"5,C"5)=11, R(P"4,P"5,C"7)=11, R(P"4,P"5,C"k)=k+2 for k>=23; R(P"4,P"6,C"4)=8, R(P"4,P"6,C"3)=R(P"4,P"6,C"5)=R(P"4,P"6,C"7)=13, R(P"4,P"6,C"k)=k+3 for k>=18.

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