The computational complexity of the backbone coloring problem for bounded-degree graphs with connected backbones

Given a graph G, a spanning subgraph H of G and an integer λ≥2, a λ-backbone coloring of G with backbone H is a proper vertex coloring of G using colors 1,2,…, in which the color difference between vertices adjacent in H is greater than or equal to λ. The backbone coloring problem is that of finding...

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Vydané v:Information processing letters Ročník 115; číslo 2; s. 232 - 236
Hlavní autori: Janczewski, Robert, Turowski, Krzysztof
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Amsterdam Elsevier B.V 01.02.2015
Elsevier Sequoia S.A
Predmet:
Backbone
Backbone chromatic number
Bounded-degree graphs
Classification
Coloring
Complexity
Computation
Computer science
Graph algorithms
Graph theory
Graphs
Integer programming
Mathematical problems
Optimization
Polynomials
Studies
Bounded-degree graphs
Backbone chromatic number
Graph algorithms
ISSN:0020-0190, 1872-6119
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Shrnutí:Given a graph G, a spanning subgraph H of G and an integer λ≥2, a λ-backbone coloring of G with backbone H is a proper vertex coloring of G using colors 1,2,…, in which the color difference between vertices adjacent in H is greater than or equal to λ. The backbone coloring problem is that of finding such a coloring whose maximum color does not exceed a given limit k. In this paper, we study the backbone coloring problem for bounded-degree graphs with connected backbones and we give a complete computational complexity classification of this problem. We present a polynomial algorithm for optimal backbone coloring for subcubic graphs with arbitrary backbones. We also prove that the backbone coloring problem for graphs with arbitrary backbones and with fixed maximum degree (at least 4) is NP-complete. Furthermore, we show that for the special case of graphs with fixed maximum degree at least 5 and λ≥4 the problem remains NP-complete even for spanning tree backbones. •The backbone coloring problem is solvable in quadratic time for subcubic graphs.•The backbone coloring problem is NP-hard for graphs with degree greater than 4.•The backbone coloring problem is NP-hard for tree backbones with bounded degree.
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ISSN:0020-0190
1872-6119
DOI:10.1016/j.ipl.2014.09.018