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 language | English |
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Pages (from-to) | 64-72 |
Number of pages | 9 |
Journal | Theoretical Computer Science |
Volume | 532 |
DOIs | |
Publication status | Published - 2014 Jan 1 |
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)