Given a vertex-colored graph, we say path is rainbow vertex if all its internal vertices have distinct colors. The graph vertex-connected there between every pair of vertices. In the Rainbow Vertex Coloring (RVC) problem want to decide whether given can be colored with at most k colors so that becomes vertex-connected. This known NP -complete even in very restricted scenarios, and few efficient...

In graph coloring, one assigns a color to each vertex of a graph so that neighboring vertices get different colors. We shall talk about a bioconsensus problem relating to graph coloring and discuss the applicability of the ideas to the DNA physical mapping problem. In many applications of graph coloring, one gathers data about the acceptable colors at each vertex. A list coloring is a graph col...

Reconfiguration problems arise when we wish to find a step-by-step transformation between two feasible solutions of a problem such that all intermediate results are also feasible. Recently, Ito et al. [5] proposed a framework of reconfiguration problems, and gave complexity and approximability results for reconfiguration problems derived from several well-known problems, such as independent set...

In this note, we show that some problems related to the length of the longest simple path from a given vertex in a graph are NP-complete. We also discuss an extension to the graph coloring problem. @ 2004 Elsevier Ltd. All rights reserved. Keywords-Longest path, Graph coloring, Complexity.

Designing effective exact algorithms for graph coloring problem is still an interesting topic. Instead of getting only one best solution, two exact graph coloring algorithms, PexaCol (Partial best solutions Exact graph Coloring algorithm) and AexaCol (All best solutions Exact graph Coloring algorithm), have been proposed, which are able to obtain a best solution subset and all best solutions re...

Genetic programming (GP) is a novel paradigm that simulates the way of solving problems by nature according to Darwin's theory of fitness-driven natural selection. Instead of using bit strings as in genetic algorithm (GA), GP uses tree structures as its computing structures. As computer programs can be represented as trees, GP has been employed as a method of generating computer programs. In th...

Our work becomes integrated into the general problem of the stability of the network ad hoc. Some, works attacked(affected) this problem. Among these works, we find the modelling of the network ad hoc in the form of a graph. Thus the problem of stability of the network ad hoc which corresponds to a problem of allocation of frequency amounts to a problem of allocation of colors in the vertex of ...