Abstract
Let x1(G) denote the edge chromatic number of the graph G. For any positive integer m and any graph G, the mixed Ramsey number x1(m,G) is defined as the least positive integer p such that if H is any graph of order p, then either x1(H) ≥ m or \(\overline H\)contains a subgraph isomorphic to G. The number x1(m,G) is investigated for certain classes of graphs G, including star graphs, complete graphs, paths, and cycles.
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