On some Ramsey numbers of unicyclic graphs (Q2765164)

Let \(R_k(G)\) denote the least number \(r\) such that any coloring of the edges of the complete graph \(K_r\) by \(k\) colors admits a copy of \(G\) with all of its edges assigned the same color. The authors prove that, if \(G\) is a unicyclic graph with odd girth, then \(R_k(G)\geq 2R_{k-1}(G)- 1\), \(k\geq 2\). They also compute some specific values for \(R_k(G)\) in the case that \(G\) is a unicyclic graph with odd girth.