We study a simple Markov chain, known as the Glauber dynamics, for randomly sampling (proper) k-colorings of an input graph G on n vertices with maximum degree ∆ and girth g. We...
A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping from V (G) to V (H), that is (x)(y) is an arc in H whenever xy is an arc in G. The orie...
We consider the class of graphs that contain no bull, no odd hole, and no antihole of length at least five. We present a new algorithm that colors optimally the vertices of every g...
We show that the conjectures by Matthews and Sumner (every 4-connected claw-free graph is hamiltonian), by Thomassen (every 4-connected line graph is hamiltonian) and by Fleischne...
A Meyniel graph is a graph in which every odd cycle of length at least five has two chords. We present a linear-time algorithm that colors optimally the vertices of a Meyniel grap...