Determining the L(2,1)-Span in Polynomial Space

  • Konstanty Junosza-Szaniawski
  • Jan Kratochvíl
  • Mathieu Liedloff
  • Paweł Rzążewski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7551)

Abstract

An 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. Moreover, a new interesting extremal graph theoretic problem is defined and solved.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Konstanty Junosza-Szaniawski
    • 1
  • Jan Kratochvíl
    • 2
  • Mathieu Liedloff
    • 3
  • Paweł Rzążewski
    • 1
  1. 1.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarszawaPoland
  2. 2.Department of Applied Mathematics, and Institute for Theoretical Computer ScienceCharles UniversityPraha 1Czech Republic
  3. 3.Laboratoire d’Informatique Fondamentale d’OrléansUniversité d’OrléansOrléans Cedex 2France

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