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...
A labeling of a graph G is distinguishing if it is only preserved by the trivial automorphism of G. The distinguishing chromatic number of G is the smallest integer k such that G ...
We propose a new exact algorithm for finding the chromatic number of a graph G. The algorithm attempts to determine the smallest possible induced subgraph G' of G which has t...
Let S be a set of horizontal line segments, or bars, in the plane. We say that G is a bar visibility graph, and S its bar visibility representation, if there exists a one-to-one co...
Alice M. Dean, William Evans, Ellen Gethner, Joshu...
: Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player ...