Determining the L(2,1)-span in polynomial space

A k-L(2,1)-labeling of a graph is a mapping from its vertex set into a set of integers {0,…,k} such that adjacent vertices get labels that differ by at least 2 and vertices in distance 2 get different labels. The main result of the paper is an algorithm finding an optimal L(2,1)-labeling of a graph (i.e. an L(2,1)-labeling in which the largest label is the least possible) in time O∗(7.4922n) and polynomial space. Then we adapt our method to obtain a faster algorithm for k-L(2,1)-labeling, where k is a small positive constant. Moreover, a new interesting extremal graph theoretic problem is defined and solved.