Coloring powers of planar graphs

We give nontrivial bounds for the inductiveness or degeneracy of power graphs Gk of a planar graph G. This implies bounds for the chromatic number as well, since the inductiveness naturally relates to a greedy algorithm for vertex-coloring the given graph. The inductiveness moreover yields bounds for the choosability of the graph. We show that the inductiveness of a square of a planar graph G is at most 9/5 , for the maximum degree sufficiently large, and that it is sharp. In general, we show for a fixed integer k 1 the inductiveness, the chromatic number, and the choosability of Gk to be O( k/2 ), which is tight. Key words. distance-2 coloring, radio coloring AMS subject classifications. 05C15, 05C85 DOI. 10.1137/S0895480100367950

• Type: Conference
• Year: 2000
• Where: SODA
• Authors: Geir Agnarsson, Magnús M. Halldórsson
• Keywords: Algorithms, Chromatic Number, Planar Graph, Planar Graph G, SODA 2000