For a fixed simple digraph F and given D , an - free k -coloring of is vertex-coloring in which no induced copy monochromatic. We study the complexity deciding for whether admits -free -coloring. Our main focus on restriction problem to planar input digraphs, where it only interesting cases ? { 2 3 } . From known results follows that every whose underlying graph not forest, 2-coloring, with ? (...

We consider the problem of list edge coloring for planar graphs. Edge coloring is the problem of coloring the edges while ensuring that two edges that are incident receive different colors. A graph is k-edge-choosable if for any assignment of k colors to every edge, there is an edge coloring such that the color of every edge belongs to its color assignment. Vizing conjectured in 1965 that every...

In this paper, we proposed an improved cuckoo search optimization (ICS) algorithm for solving planar graph coloring problem. The improved cuckoo search optimization algorithm is consisting of the walking one strategy, swap and inversion strategy and greedy strategy. The proposed improved cuckoo search optimization algorithm can solve the planar graph coloring problem using four-colors more effi...

The problem of edge coloring a bipartite graph is to color the edges so that adjacent edges receive di erent colors An optimal algorithm uses the minimum number of colors to color the edges We consider several approximation algorithms for edge coloring bipartite graphs and show tight bounds on the number of colors they use in the worst case We also present results on the constrained edge colori...

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 ...

The H-Coloring problem can be expressed as a particular case of the Constraint Satisfaction Problem (CSP) whose computational complexity has been intensively studied under various approaches in the last several years. We show that the dichotomy theorem proved by P.Hell and J.Nešetřil [12] for the complexity of the H-Coloring problem for undirected graphs can be obtained using general methods fo...