A complete characterization of the zero-sum (mod 2) Ramsey numbers (Q1336447)

The zero-sum (mod 2) Ramsey number of a graph \(G\) is the smallest integer \(t\) such that in every edge coloring of the complete graph on \(t\) vertices with colors zero and one, there is a copy of \(G\) containing an even number of ones. The author determines zero-sum Ramsey numbers for all graphs with an even number of edges. Suppose that \(G\) is such a graph of order \(n\). Then the zero-sum Ramsey number is \(n+2\) if \(G\) is complete; \(n+1\) if \(G\) is the union of two complete graphs or if all degrees in \(G\) are odd; \(n\) otherwise.