Given a graph G = (V, E) and positive integral vertex weights w : V → N, the max-coloring problem seeks to find a proper vertex coloring of G whose color classes C1, C2, . . . ,...
A homomorphism from an oriented graph G to an oriented graph H is an arc-preserving mapping f from V(G) to V(H), that is f(x)f(y) is an arc in H whenever xy is an arc in G. The or...
A coloring is proper if each color class induces connected components of order one (where the order of a graph is its number of vertices). Here we study relaxations of proper two-c...
The sum of a coloring is the sum of the colors assigned to the vertices (assuming that the colors are positive integers). The sum (G) of graph G is the smallest sum that can be ach...
Abstract. The paper describes an application of Parallel Simulated Annealing (PSA) for solving one of the most studied NP-hard optimization problems: Graph Coloring Problem (GCP). ...
Szymon Lukasik, Zbigniew Kokosinski, Grzegorz Swie...