An analysis between different algorithms for the graph vertex coloring problem

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...

An edge coloring problem for graph products

The edges of the Cartesian product of graphs G x Hare to be colored with the condition that all rectangles, i.e., K2 x K2 subgraphs, must be colored with four distinct colors. The minimum number of colors in such colorings is determined for all pairs of graphs except when G is 5-chromatic and H is 4or 5-chromatic.

Polynomial Cases for the Vertex Coloring Problem

The computational complexity of the Vertex Coloring problem is known for all hereditary classes of graphs defined by forbidding two connected five-vertex induced subgraphs, except for seven cases. We prove the polynomial-time solvability of four of these problems: for (P5, dart)-free graphs, (P5, banner)-free graphs, (P5, bull)-free graphs, and (fork, bull)-free graphs.