Ramsey numbers for sets of small graphs
Define the Ramsey number for sets of graphs \(r=r(G_ 1-G_ 2-\cdots- G_ m,H_ 1-H_ 2-\cdots-H_ n)\) to be the smallest \(r\), such that every 2-coloring of the edges of the complete graph \(K_ r\) contains a subgraph \(G_ i\) with all edges of one color, or a subgraph \(H_ i\) with all edges of the other color. The authors show all 508 Ramsey numbers: (i) for all sets of graphs with at most \(H\) vertices (198), (ii) in the diagonal case \((m=n\), \(G_ i=H_ i)\) for all pairs of graphs, one with at most 4 and one with 5 vertices (65), (iii) in the diagonal case for all sets of graphs with 5 vertices (245).
scientific article; zbMATH DE number 562649
scientific article