A note on maximum differential coloring of planar graphs

M. A. Bekos, M. Kaufmann, S. Kobourov, S. Veeramoni

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We study the maximum differential coloring problem, where the vertices of an n-vertex graph must be labeled with distinct numbers ranging from 1to n, so that the minimum absolute difference between two labels of any two adjacent vertices is maximized. As the problem isNP-hard forgeneral graphs[16], we consider planar graphs and subclasses thereof. We prove that the maximum differential coloring problem remainsNP-hard, even for planar graphs. We also present tight bounds for regular caterpillars and spider graphs. Using these new bounds, we prove that the Miller-Pritikin labeling scheme[19]for forests is optimal for regular caterpillars and for spider graphs.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalJournal of Discrete Algorithms
Volume29
Issue numberC
DOIs
StatePublished - 2014

Keywords

  • Antibandwidth
  • Caterpillar graph
  • Graph labeling
  • Separation number
  • Spider graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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