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 analyze Markov chains for generating a random k-coloring of a random graph Gn,d/n. When the average degree d is constant, a random graph has maximum degree (log n/ log log n), ...
Martin E. Dyer, Abraham D. Flaxman, Alan M. Frieze...
We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree dp4:03; i.e., G?n; p ? d=n?; are 3-colorable a...