Suppose G is a graph. The chromatic Ramsey number rc(G) of G is the least integer m such that there exists a graph F of chromatic number m for which the following is true: For any...
Let T be a fixed tournament on k vertices. Let D(n, T) denote the maximum number of orientations of an n-vertex graph that have no copy of T. We prove that D(n, T) = 2tk-1(n) for ...
We prove that the total chromatic number of any graph with maximum degree is at most plus an absolute constant. In particular, we show that for su ciently large, the total chromat...