On the L(h,k)-Labeling of Co-comparability Graphs

  • Tiziana Calamoneri
  • Saverio Caminiti
  • Stephan Olariu
  • Rossella Petreschi
Conference paper

DOI: 10.1007/978-3-540-74450-4_11

Volume 4614 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Calamoneri T., Caminiti S., Olariu S., Petreschi R. (2007) On the L(h,k)-Labeling of Co-comparability Graphs. In: Chen B., Paterson M., Zhang G. (eds) Combinatorics, Algorithms, Probabilistic and Experimental Methodologies. Lecture Notes in Computer Science, vol 4614. Springer, Berlin, Heidelberg

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.

Keywords

L(h and k)-Labeling co-comparability graphs interval graphs unit-interval graphs 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Tiziana Calamoneri
    • 1
  • Saverio Caminiti
    • 1
  • Stephan Olariu
    • 2
  • Rossella Petreschi
    • 1
  1. 1.Dipartimento di Informatica, Università degli Studi di Roma “La Sapienza”, Via Salaria 113, 00198 RomaItaly
  2. 2.Department of Computer Science, Old Dominion University, Norfolk,VA 23529-0162U.S.A