(Circular) backbone colouring: Forest backbones in planar graphs

被引：8

作者：

Havet, Frederic ^{[1
,2
,3
]}

King, Andrew D. ^{[4
,5
]}

Liedloff, Mathieu ^{[6
]}

Todinca, Loan ^{[6
]}

机构：

[1] UNSA, CNRS I3S, Projet Coati, Paris, France

[2] INRIA Sophia Antipolis, Sophia Antipolis, France

[3] Simon Fraser Univ, PIMS, UMI 3069, CNRS, Burnaby, BC V5A 1S6, Canada

[4] Simon Fraser Univ, Dept Math, Burnaby, BC V5A 1S6, Canada

[5] Simon Fraser Univ, Dept Comp Sci, Burnaby, BC V5A 1S6, Canada

[6] Univ Orleans, Lab Informat Fondamentale Orleans, Orleans, France

来源：

DISCRETE APPLIED MATHEMATICS | 2014年 / 169卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Backbone colouring; Planar graph; Tree backbone; NP-complete;

D O I：

10.1016/j.dam.2014.01.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Consider an undirected graph G and a subgraph H of G, on the same vertex set. The q-backbone chromatic number BBCq(G, H) is the minimum k such that G can be properly coloured with colours from {1,...,k}, and moreover for each edge of H, the colours of its ends differ by at least q. In this paper we focus on the case when G is planar and H is a forest. We give a series of NP-hardness results as well as upper bounds for BBCq(G, H), depending on the type of the forest (matching, galaxy, spanning tree). Eventually, we discuss a circular version of the problem. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：119 / 134

页数：16

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