TY - JOUR

T1 - Bandwidth consecutive multicolorings of graphs

AU - Nishikawa, Kazuhide

AU - Nishizeki, Takao

AU - Zhou, Xiao

N1 - Funding Information:
Work partly supported by MEXT-supported Program for the Strategic Research Foundation at Private Universities. Corresponding author. Tel.: +81 22 795 7166. E-mail addresses: nishikawa@kwansei.ac.jp (K. Nishikawa), nishi@kwansei.ac.jp (T. Nishizeki), zhou@ecei.tohoku.ac.jp (X. Zhou).
Publisher Copyright:
© 2013 Elsevier B.V.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Acyclic orientation

KW - Algorithm

KW - Approximation

KW - Bandwidth coloring

KW - Channel assignment

KW - FPTAS

KW - Multicoloring

KW - Partial k-tree

KW - Series-parallel graph

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U2 - 10.1016/j.tcs.2013.02.015

DO - 10.1016/j.tcs.2013.02.015

M3 - Article

AN - SCOPUS:84898054111

VL - 532

SP - 64

EP - 72

JO - Theoretical Computer Science

JF - Theoretical Computer Science

SN - 0304-3975

ER -