Abstract
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.
Publication Date
2008
Document Type
Article
Department, Program, or Center
Computer Science (GCCIS)
Recommended Citation
X. Xu, Z. Shao, and S. Radiszowski. Bounds on some Ramsey numbers invovling quadrilateral. Ars Combinatoria, 2008 (90) 337-344.
SRadziszowskiSlides2009.pdf (169 kB)
Campus
RIT – Main Campus
Comments
Note: imported from RIT’s Digital Media Library running on DSpace to RIT Scholar Works in February 2013.