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 ...

State space explosion is a fundamental obstacle in formal verification of concurrent systems. As a solution for this problem, this paper deals with distributed state space. The authors’ solution is to introduce the coloring concept and dominance relation in graphs for finding the good distribution of given graphs. This basic solution is improved in two steps: the initialization and optimization...

This paper presents an ant-based algorithm for the graph coloring problem. An important difference that distinguishes this algorithm from previous ant algorithms is the manner in which ants are used in the algorithm. Unlike previous ant algorithms where each ant colors the entire graph, each ant in this algorithm colors a small portion of the graph using only local information. These individual...

A graph is f -choosable if for every collection of lists with list sizes specified by f there is a proper coloring using colors from the lists. The sum choice number is the minimum over all choosable functions f of the sum of the sizes in f . We show that the sum choice number of a 2 × n array (equivalent to list edge coloring K2,n and to list vertex coloring the cartesian product K22Kn) is n2 ...

This paper presents a new heuristic algorithm for the graph coloring problem based on a combination of genetic algorithms and simulated annealing. Our algorithm exploits a novel crossover operator for graph coloring. Moreover, we investigate various ways in which simulated annealing can be used to enhance the performance of an evolutionary algorithm. Experiments performed on various collections...

A majority coloring of a directed graph is vertex-coloring in which every vertex has the same color as at most half its out-neighbors. Kreutzer, Oum, Seymour, van der Zypen and Wood proved that digraph $4$-coloring conjectured admits $3$-coloring. They observed Local Lemma implies conjecture for digraphs large enough minimum out-degree if, crucially, maximum in-degree bounded by a(n exponential...

Background Understanding environmental factors affecting the educational process and including them in educational planning will lead into increased outcome of education, mental health, reduced stress, and higher education performance. This study was conducted to investigate the impact of educational spaces coloring on learning and academic achievement of elementary school students in the acad...

The present two-part study examined the effects of coloring mandalas on state anxiety reduction with considerations of duration spent coloring and Big-5 personality traits. It was hypothesized that coloring mandalas for 30 minutes would significantly reduce levels of state anxiety. There were three coloring conditions that were randomly assigned to 105 participants. Measures included a Spielber...