Batch scheduling of conflicting jobs is modeled by batch coloring of a graph. Given an undirected graph and the number of colors required by each vertex, we need to find a proper batch coloring of the graph, i.e., partition the vertices to batches which are independent sets, and to assign to each batch a contiguous set of colors, whose size equals to the maximum color requirement of any vertex ...

In this paper, we propose a learning automata-based iterative algorithm for approximating a near optimal solution to the vertex coloring problem. Vertex coloring is a well-known NP-hard optimization problem in graph theory in which each vertex is assigned a color so that no two adjacent vertices have the same color. Each iteration of the proposed algorithm is subdivided into several stages, and...

A b-coloring of a graph is a coloring such that every color class admits a vertex adjacent to at least one vertex receiving each of the colors not assigned to it. The b-chromatic number of a graph G, denoted by χb(G), is the maximum number t such that G admits a b-coloring with t colors. A graph G is b-continuous if it admits a b-coloring with t colors, for every t = χ(G), . . . , χb(G), and it...

Despite the fact that some vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not “under control” from a polyhedral point of view. The equivalence between optimization and polyhedral separation suggests that, for these problems, there must exist formulations admitting some elegant characterization for the polytopes associated to them. Therefo...

Despite the fact that many vertex coloring problems are polynomially solvable on certain graph classes, most of these problems are not “under control” from a polyhedral point of view. The equivalence between optimization and separation suggests the existence of integer programming formulations for these problems whose associated polytopes admit elegant characterizations. In this work we address...

In this paper, we introduce and study a new coloring problem of a graph called the dominated coloring. A dominated coloring of a graph G is a proper vertex coloring of G such that each color class is dominated by at least one vertex of G. The minimum number of colors among all dominated colorings is called the dominated chromatic number, denoted by χdom(G). In this paper, we establish the close...