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...
We are interested in the graph coloring problem. We propose an exact method based on a linear-decomposition of the graph. The complexity of this method is exponential according to...