Sub-Ramsey numberRainbow matchingsLocal lemmaGiven a graph G and a positive integer k, the sub-Ramsey number sr(G, k) is defined to be the minimum number m such that every \\(K_{m}\\) whose edges are colored using every color at most k times contains a subgraph isomorphic to G ...
Since the Ramsey number R(3,3) is 6, every graph G of order at least 6 that does not contain 3K1 as an induced subgraph, satisfies ω(G)≥3. 5. Matchings in cubic graphs with specified odd girth The following results are interesting byproducts of our research. For every odd integer...