Bandwidth consecutive multicolorings of graphs

Kazuhide Nishikawa, Takao Nishizeki, Xiao Zhou

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

Let G be a simple graph in which each vertex v has a positive integer weight b(v) and each edge (v, w) has a nonnegative integer weight b(v, w). A bandwidth consecutive multicoloring of G assigns each vertex v a specified number b(v) of consecutive positive integers so that, for each edge (v, w), all integers assigned to vertex v differ from all integers assigned to vertex w by more than b(v, w). The maximum integer assigned to a vertex is called the span of the coloring. In the paper, we first investigate fundamental properties of such a coloring. We then obtain a pseudo polynomial-time exact algorithm and a fully polynomial-time approximation scheme for the problem of finding such a coloring of a given series-parallel graph with the minimum span. We finally extend the results to the case where a given graph G is a partial k-tree, that is, G has a bounded tree-width.

Original languageEnglish
Pages (from-to)64-72
Number of pages9
JournalTheoretical Computer Science
Volume532
DOIs
Publication statusPublished - 2014

Keywords

  • Acyclic orientation
  • Algorithm
  • Approximation
  • Bandwidth coloring
  • Channel assignment
  • FPTAS
  • Multicoloring
  • Partial k-tree
  • Series-parallel graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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