Pushable homomorphisms and the pushable chromatic number χp of oriented graphs were introduced by Klostermeyer MacGillivray in 2004. They notably observed that, for any graph G⃗, we have χp(G⃗)≤χo(G⃗)≤2χp(G⃗), where χo(G⃗) denotes G⃗. This stands as first general bounds on χp. parameter was further studied later works. work is dedicated to fulfilling particular degree conditions. For all Δ≥29, prove ...

In this paper, we obtain polynomial time algorithms to determine the acyclic chromatic number, the star chromatic number and the harmonious chromatic number of P4-tidy graphs and (q, q − 4)-graphs, for every fixed q. These classes include cographs, P4-sparse and P4-lite graphs. We also obtain a polynomial time algorithm to determine the Grundy number of (q, q − 4)-graphs. All these coloring pro...

The main goal of this paper is to formalize and explore a connection between chromatic properties of graphs with geometric representations and competitive analysis of on-line algorithms, which became apparent after the recent construction of triangle-free geometric intersection graphs with arbitrarily large chromatic number due to Pawlik et al. We show that on-line graph coloring problems give ...