L(h,1,1)-Labeling of Outerplanar Graphs

An L(h,1,1)-labeling of a graph is an assignment of labels from the set of integers {0, ... , l} to the vertices of the graph such that adjacent vertices are assigned integers of at least distance h >= 1 apart and all vertices of distance three or less must be assigned different labels. The aim of the L(h,1,1)-labeling problem is to minimize l. This minimum is denoted by lambda_{h,1,1} and called span of the L(h,1,1)-labeling. As outerplanar graphs have bounded treewidth, the L(1,1,1)-labeling problem on outerplanar graphs can be exactly solved in O(n^3), where the multiplicative constant is exponential in Delta. In this paper we give a linear time approximation algorithm for computing the more general L(h,1,1)-labeling for outerplanar graphs that is within additive constants of the optimum values.

Conference Version