TY - JOUR
T1 - Bandwidth consecutive multicolorings of graphs
AU - Nishikawa, Kazuhide
AU - Nishizeki, Takao
AU - Zhou, Xiao
PY - 2014/1/1
Y1 - 2014/1/1
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 -