Algorithms for the rainbow vertex coloring problem on graph classes

On the Maximum Number of Dominating Classes in Graph Coloring

In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

Complexity of Rainbow Vertex Connectivity Problems for Restricted Graph Classes

A path in a vertex-colored graph G is vertex rainbow if all of its internal vertices have a distinct color. The graph G is said to be rainbow vertex connected if there is a vertex rainbow path between every pair of its vertices. Similarly, the graph G is strongly rainbow vertex connected if there is a shortest path which is vertex rainbow between every pair of its vertices. We consider the comp...

Automatically Generated Algorithms for the Vertex Coloring Problem

The vertex coloring problem is a classical problem in combinatorial optimization that consists of assigning a color to each vertex of a graph such that no adjacent vertices share the same color, minimizing the number of colors used. Despite the various practical applications that exist for this problem, its NP-hardness still represents a computational challenge. Some of the best computational r...

Stochastic Local Search Algorithms for the Graph Coloring Problem

Complete and Incomplete Algorithms for the Queen Graph Coloring Problem

The queen graph coloring problem consists in covering a n × n chessboard with n queens, so that two queens of the same color cannot attack each other. When the size, n, of the chessboard is a multiple of 2 or 3, it is hard to color the queen graph with only n colors. We have developed an exact algorithm which is able to solve exhaustively this problem for dimensions up to n = 12 and find one so...