Elegant distance constrained labelings of trees

Abstract

In our contribution to the study of graph labelings with three distance constraints we introduce a concept of elegant labelings: labelings where labels appearing in a neighborhood of a vertex can be completed into intervals such that these intervals are disjoint for adjacent vertices. We justify introduction of this notion by showing that use of these labelings provides good estimates for the span of the label space, and also provide a polynomial time algorithm to find an optimal elegant labeling of a tree for distance constraints (p, 1, 1). In addition several computational complexity issues are discussed. © Springer-Verlag 2004.