DOIAbstract
AbstractIn [2, 3], Chung and Liu introduce the following generalization of Ramsey Theory for graphs. Choose c colors, and integers d1, d2,…, dn satisfying 1⩽d1<d2<⋯<dn <c. Order the (cd1) subsets of d1 colors, (cd2) subsets of d2 colors,…,(cd2) subsets of dn colors and let t=∑i(cdi. For graphs G1, G2,…, G3, the (d1, d2,…,dn)-chromatic Ramsey number denoted by Rcd1, d2, …, dn(G1, G2, …, Gt), is the smallest integer p such that if the edges of Kp are colored with c colors in any fashion, then for some i the subgraph whose edges are colored with the ith subset of colors contains Gi. The numbers R21(G1, G2), simply denoted R(G1, G2), have been surveyed in [1] and in particular if G1, G2,…, Gc are complete graphs, then Rc1(G1, G2,…, Gc), denoted...
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