A Study of Tabu Search for Coloring Random 3-Colorable Graphs Around the Phase Transition

Abstract

The authors present an experimental investigation of tabu search (TS) to solve the 3-coloring problem (3-COL). Computational results reveal that a basic TS algorithm is able to find proper 3-colorings for random 3-colorable graphs with up to 11000 vertices and beyond when instances follow the uniform or equipartite well-known models, and up to 1500 vertices for the hardest class of flat graphs. This study also validates and reinforces some existing phase transition thresholds for 3-COL.