Algorithms for bandwidth consecutive multicolorings of graphs

  • Authors:

  • Kazuhide Nishikawa;Takao Nishizeki;Xiao Zhou

  • Affiliations:

  • School of Science and Engineering, Kwansei Gakuin University, Sanda-shi, Hyogo, Japan;School of Science and Engineering, Kwansei Gakuin University, Sanda-shi, Hyogo, Japan;Graduate School of Information Sciences, Tohoku University, Sendai-shi, Miyagi, Japan

  • Venue:
  • FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2012

Quantified Score

Hi-index 0.00

Visualization

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.