Coloring certain proximity graphs

Abstract

We examine the graph coloring problem for three families of Euclidean proximity graphs. Results include a linear-time 4-coloring algorithm for relative neighborhood graphs, a linear-time 3-coloring method for 3-chromatic Delaunay graphs, and two minimum-coloring heuristics for Gabriel graphs. The heuristics are shown to outperform other coloring methods when applied to these graphs. We also show that the 3-colorability problem for Delaunay graphs is polynomial-time solvable.