We study the function f G de ned for a graph G as the smallest integer k such that the join ofG with a stable set of size k is not jV G j choosable This function was introduced recently in order to describe extremal graphs for a list coloring version of a famous inequality due to Nordhaus and Gaddum Some bounds and some exact values for f G are determined

Matrix partitioning problems that arise in the efficient estimation of sparse Jacobians and Hessians can be modeled using variants of graph coloring problems. In a previous work [6], we argue that distance-2 and distance3 2 graph coloring are robust and flexible formulations of the respective matrix estimation problems. The problem size in large-scale optimization contexts makes the matrix esti...

We study the performance of the algorithms First-Fit and Next-Fit for two online edge coloring problems. In the min-coloring problem, all edges must be colored using as few colors as possible. In the max-coloring problem, a fixed number of colors is given, and as many edges as possible should be colored. Previous analysis using the competitive ratio has not separated the performance of First-Fi...

This paper proposes a new method based on the cultural algorithm to solve graph coloring problem (GCP). Graph coloring problem involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In this paper various components of cultural algorithm have been implemented to solve GCP with a self adaptive behavior in an efficient manner...

This paper proposes a new method based on the cultural algorithm to solve graph coloring problem (GCP). Graph coloring problem involves finding the minimum number of colors for coloring the graph vertices such that adjacent vertices have distinct colors. In this paper various components of cultural algorithm have been implemented to solve GCP with a self adaptive behavior in an efficient manner...

In this paper, we study the conflict-free coloring of graphs induced by neighborhoods. A coloring of a graph is conflict-free if every vertex has a uniquely colored vertex in its neighborhood. The conflict-free coloring problem is to color the vertices of a graph using the minimum number of colors such that the coloring is conflict-free. We consider both closed neighborhoods, where the neighbor...

Nous étudions le problème de coloration probabiliste (PCOLOR) sous une stratégie de modification consistant, pour une solution a priori C, de supprimer les sommets qui son absents de C. Nous calculons la fonction objectif associée avec cette stratégie, donnons des bornes pour sa valeur et caractérisons la complexité algorithmique du calcul de la solution a priori optimal. Nous démontrons que PC...

Let G = (V,E) be a simple and connected graph. The graph coloring problem on G is to color the vertices of G such that the colors of any two adjacent vertices are different and the number of used colors is as small as possible. By assigning a positive integer to a color, the sum coloring problem asks the minimum sum of the coloring numbers assigned for all vertices. In this paper, we introduce ...

We consider max coloring on hereditary graph classes. The problem is defined as follows. Given a graph G = (V, E) and positive node weights w : V → (0,∞), the goal is to find a proper node coloring of G whose color classes C1, C2, . . . , Ck minimize k ∑ i=1 maxv∈Ci w(v). We design a general framework which allows to convert approximation algorithms for standard node coloring into algorithms fo...

This paper surveys the most important algorithmic and computational results on the Vertex Coloring Problem (VCP) and its generalizations. The first part of the paper introduces the classical models for the VCP, and discusses how these models can be used and possibly strengthened to derive exact and heuristic algorithms for the problem. Computational results on the best performing algorithms pro...