We study a simple Markov chain, known as the Glauber dynamics, for generating a random k-coloring of a n-vertex graph with maximum degree . We prove that, for every > 0, the d...
Martin E. Dyer, Alan M. Frieze, Thomas P. Hayes, E...
We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness ...
For a graph G and an integer t we let mcct(G) be the smallest m such that there exists a coloring of the vertices of G by t colors with no monochromatic connected subgraph having ...
We introduce and study adapted list coloring of graphs and hypergraphs. This is a generalization of ordinary list coloring and adapted coloring, and has more applications than thes...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...