For graphs G_1,G_2,...,G_m the Ramsey number R(G_1,G_2,...,G_m) is defined to be the smallest integer n such that any m-coloring of the edges of the complete graph K_n must include a monochromatic G_i in color i, for some i. In this note we establish several lower and upper bounds for some Ramsey numbers involving quadrilateral C_4, including R(C_4,K_9) < = 32, 19 < = R(C_4,C_4,K_4) < = 22, 31 < = R(C_4,C_4,C_4,K_4) < = 50, 52 < = R(C_4,K_4,K_4) < = 72, 42 < = R(C_4,C_4,K_3,K_4) < = 76, and 87 < = (C_4,C_4,K_4,K_4) < = 179.
Department, Program, or Center
Computer Science (GCCIS)
X. Xu, Z. Shao, and S. Radiszowski. Bounds on some Ramsey numbers invovling quadrilateral. Ars Combinatoria, 2008 (90) 337-344.
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