We consider the sum coloring (chromatic sum) and sum multi-coloring problems for restricted families of graphs. In particular, we consider the graph classes of proper intersection graphs of axis-parallel rectangles, proper interval graphs, and unit disk graphs. All the above mentioned graph classes belong to a more general graph class of (k+1)clawfree graphs (respectively, for k = 4, 2, 5). We ...

In a previous work, we proposed a new integer programming formulation for the graph coloring problem which, to a certain extent, avoids symmetry. We studied the facet structure of the 0/1-polytope associated with it. Based on these theoretical results, we present now a Branch-and-Cut algorithm for the graph coloring problem. Our computational experiences compare favorably with the well-known ex...

Graph coloring has been studied for a long time and continues to receive interest within the research community [43]. It has applications in scheduling [46], timetables, and compiler register allocation [45]. The most popular variant of graph coloring, k-coloring, can be thought of as an assignment of k colors to the vertices of a graph such that adjacent vertices are assigned different colors....