the robust coloring problem (rcp) is a generalization of the well-known graph coloring problem where we seek for a solution that remains valid when extra edges are added. the rcp is used in scheduling of events with possible last-minute changes and study frequency assignments of the electromagnetic spectrum. this problem has been proved as np-hard and in instances larger than 30 vertices, meta-...

The Grundy number of a graph is the maximum number of colors used by the greedy coloring algorithm over all vertex orderings. In this paper, we study the computational complexity of Grundy Coloring, the problem of determining whether a given graph has Grundy number at least k. We also study the variants Weak Grundy Coloring (where the coloring is not necessarily proper) and Connected Grundy Col...

A subset D of the vertex set V (G) of a graph G is called dominating in G, if each vertex of G either is in D, or is adjacent to a vertex of D. If moreover the subgraph 〈D〉 of G induced by D is regular of degree 1, then D is called an induced-paired dominating set in G. A partition of V (G), each of whose classes is an induced-paired dominating set in G, is called an induced-paired domatic part...

An upper dominating set in a graph is a minimal (with respect to set inclusion) dominating set of maximum cardinality. The problem of finding an upper dominating set is NP-hard for general graphs and in many restricted graph families. In the present paper, we study the computational complexity of this problem in monogenic classes of graphs (i.e. classes defined by a single forbidden induced sub...

In this paper we investigate the total coloring number for double vertex graphs of some of the most common classes of graphs. Mathematics Subject Classification: 05C15

In this paper, we consider the topological interference management (TIM) problem in a dynamic setting, where an adversary perturbs network topology to prevent exploitation of sophisticated coding opportunities (e.g., alignment). Focusing on special class – chordal networks investigate algorithmic aspects TIM under adversarial perturbation. particular, given perturbation with respect edge insert...

Given a coloring of the vertices, we say subgraph H is monochromatic if every vertex of H is assigned the same color, and rainbow if no pair of vertices of H are assigned the same color. Given a graph G and a graph F , we define an F -WORM coloring of G as a coloring of the vertices of G without a rainbow or monochromatic subgraph H isomorphic to F . We present some results on this concept espe...

A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k − 1 color classes. The b-chromatic number φ(G) of a graph G is the maximum k for which G has a b-coloring by k colors. This concept was introduced by R.W. Irving and D.F. Manlove in 1999. In this paper we study the b-chromatic ...

Graph coloring is one of the most studied combinatorial optimization problems. This paper presents an improved extraction and expansion method (IE2COL) initially introduced in [47]. IE2COL employs a forward independent set extraction strategy to reduce the initial graph G. From the reduced graph, IE2COL triggers a backward coloring process which uses extracted independent sets as new color clas...

A b-coloring of a graph G by k colors is a proper k-coloring of the vertices of G such that in each color class there exists a vertex having neighbors in all the other k − 1 color classes. The b-chromatic number χb(G) of a graph G is the largest integer k such that G admits a b-coloring by k colors. We present some lower bounds for the b-chromatic number of connected bipartite graphs. We also d...