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...
We consider the Chromatic Sum Problem on bipartite graphs which appears to be much harder than the classical Chromatic Number Problem. We prove that the Chromatic Sum Problem is NP...
Michal Malafiejski, Krzysztof Giaro, Robert Jancze...
A homomorphism from an oriented graph G to an oriented graph H is a mapping from the set of vertices of G to the set of vertices of H such that ----(u)(v) is an arc in H whenever...
We show how to use split decomposition to compute the weighted clique number and the chromatic number of a graph and we apply these results to some classes of graphs. In particular...
The circular chromatic number of a graph is a well-studied refinement of the chromatic number. Circular-perfect graphs is a superclass of perfect graphs defined by means of this...