For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic G.Define Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤t.It is shown that f(...For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic G.Define Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤t.It is shown that f(G;t)≤cn for p-arrangeable graphs with n vertices,where p≥1,c=c(p)and t=t(p)are positive constants.展开更多
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文摘For graphs F and G,let F→(G,G)denote that any red/blue edge coloring of F contains a monochromatic G.Define Folkman number f(G;t)to be the smallest order of a graph F such that F→(G,G)andω(F)≤t.It is shown that f(G;t)≤cn for p-arrangeable graphs with n vertices,where p≥1,c=c(p)and t=t(p)are positive constants.
