On Graph Coloring Analysis Through Visualization

Abstract

The focus of the presented article is put on the analysis of edge coloring of selected sets of graphs - we are specifically interested in edge 3-coloring of graphs called snarks. Previous research suggests, that while using a single coloring algorithm and using various initial graph coloring edges, coloring of such graph may take anywhere from time lower than one millisecond to the time ranging in hundreds of milliseconds. In our case, we use recursive backtracking coloring algorithm based on breadth-first search and implement the change of initial graph coloring edge via permutation of adjacency matrix of graph. In this article, we present a tool created for the needs of analysis of edge coloring of graphs which is based on visualization of edge coloring and we present several problematic subgraphs and patterns which increase the time of edge coloring of cubic graphs.