We investigate a coloring problem, called ordered coloring, in grids and some other families of grid-like graphs. Ordered coloring (also known as vertex ranking) is related to conflict-free coloring and other traditional coloring problems. Such coloring problems can model (among others) efficient frequency assignments in cellular networks. Our main technical results improve upper and lower boun...

In this paper we propose a deterministic parallel graph coloring algorithm that enables Multi-Coloring in parallel for sparse undirected graphs by coarse-grained segmentation and auxiliary graph coloring. The proposed algorithm is implemented and tested on standard problem instances from engineering applications and benchmarked against various relevant deterministic graph coloring algorithms. Q...

Graph vertex coloring is one of the most studied NP-hard combinatorial optimization problems. Given the hardness of the problem, various heuristic algorithms have been proposed for practical graph coloring, based on local search, population-based approaches and hybrid methods. The research in graph coloring heuristics is very active and improved results have been obtained recently, notably for ...

Graph coloring and its generalizations are useful tools in modeling a wide variety of scheduling and assignment problems. In this paper we review several variants of graph coloring, such as precoloring extension, list coloring, multicoloring, minimum sum coloring, and discuss their applications in scheduling.

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by using not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NP-hardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line graphs, comparability graphs and general graphs. This provide...

A proper coloring of a graph is odd if every non-isolated vertex has some color that appears an number times on its neighborhood. This notion was recently introduced by Petruševski and Škrekovski, who proved planar admits 9-coloring; they also conjectured 5-coloring. Shortly after, this conjecture confirmed for graphs girth at least seven Cranston; outerplanar Caro, Petruševski, Škrekovski. Bui...

Graph coloring has numerous applications and is a wellknown NP-complete problem. The goal of this paper is to survey recent results of the authors on coloring and improper coloring of sparse graphs and to point out some polynomial-time algorithms for coloring (not necessarily optimal) of graphs with bounded maximum average degree. Mathematics Subject Classification: 05C15, 05C35

An adjacent vertex distinguishing edge-coloring or an avd-coloring of a simple graph G is a proper edge-coloring of G such that no pair of adjacent vertices meets the same set of colors. We prove that every graph with maximum degree ∆ and with no isolated edges has an avd-coloring with at most ∆ + 300 colors, provided that ∆ > 1020. AMS Subject Classification: 05C15

We prove that the intersection hypergraph of a family of n pseudo-disks with respect to another family of pseudo-disks admits a proper coloring with 4 colors and a conflict-free coloring with O(log n) colors. Along the way we prove that the respective Delaunay-graph is planar. We also prove that the intersection hypergraph of a family of n regions with linear union complexity with respect to a ...