Fast exact algorithm for L(2,1)-labeling of graphs

Abstract

An L(2,1)-labeling of a graph is a mapping from its vertex set into nonnegative integers such that the labels assigned to adjacent vertices differ by at least 2, and labels assigned to vertices of distance 2 are different. The span of such a labeling is the maximum label used, and the L(2,1)-span of a graph is the minimum possible span of its L(2,1)-labelings. We show how to compute the L(2,1)-span of a connected graph in time O*(2.6488 n). Previously published exact exponential time algorithms were gradually improving the base of the exponential function from 4 to the so far best known 3.2361, with 3 seemingly having been the Holy Grail. © 2011 Springer-Verlag.