On the L(h, k)-labeling of co-comparability graphs

  • Authors:

  • Tiziana Calamoneri;Saverio Caminiti;Stephan Olariu;Rossella Petreschi

  • Affiliations:

  • Dipartimento di Informatica, Università degli Studi di Roma "La Sapienza", Roma, Italy;Dipartimento di Informatica, Università degli Studi di Roma "La Sapienza", Roma, Italy;Department of Computer Science, Old Dominion University, Norfolk, VA;Dipartimento di Informatica, Università degli Studi di Roma "La Sapienza", Roma, Italy

  • Venue:
  • ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
  • Year:
  • 2007

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Abstract

Given two non negative integers h and k, an L(h, k)-labeling of a graph G = (V, E) is a map from V to a set of labels such that adjacent vertices receive labels at least h apart, while vertices at distance at most 2 receive labels at least k apart. The goal of the L(h, k)-labeling problem is to produce a legal labeling that minimizes the largest label used. Since the decision version of the L(h, k)-labeling problem is NP-complete, it is important to investigate classes of graphs for which the problem can be solved efficiently. Along this line of though, in this paper we deal with co-comparability graphs and two of its subclasses: interval graphs and unit-interval graphs. Specifically, we provide, in a constructive way, the first upper bounds on the L(h, k)-number of co-comparability graphs and interval graphs. To the best of our knowledge, ours is the first reported result concerning the L(h, k)-labeling of co-comparability graphs. In the special case where k = 1, our result improves on the best previously-known approximation ratio for interval graphs.