Vrcholová barvení grafů

Abstract

In this bachelor thesis I am dealing with vertex colorings of simple graphs with focus on vertex coloring algorithms. A proper vertex m - coloring of a graph is an assignment of m colors to the vertices so that, no two adjacent vertices share a color. The problem of the proper vertex m - coloring of a graph is well known to be an NP - complete problem for m ≥ 3. So far, no algorithm can solve this problem generaly in polynomial time (we assume that P ≠ NP). I present a heuristic algorithm based on the greedy coloring and it's optimized version, then example of deterministic algorithm is examined. I compare these algorithms and on simple examples show their principles and functionality.