Complexity of greedy edge-colouring

The Grundy index of a graph G =(V, E ) is the greatest number of colours that the greedy edge-colouring algorithm can use on G . We prove that the problem of determining the Grundy index of a graph G=(V, E ) is NP-hard for general graphs. We also show that this problem is polynomial-time solvable fo...

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Veröffentlicht in:Journal of the Brazilian Computer Society Jg. 21; H. 1; S. 1
Hauptverfasser: Havet, Frédéric, Maia, A. Karolinna, Yu, Min-Li
Format: Journal Article
Sprache:Englisch
Veröffentlicht: London Springer London 01.12.2015
Sociedade Brasileira de Computação
Springer Verlag
Schlagworte:
Computer Science
Computer System Implementation
Data Structures
Discrete Mathematics
Graph theory and algorithms: Fifth Latin-American Workshop on Cliques in Graphs
Operating Systems
Simulation and Modeling
Chromatic Number
Channel Assignment
Line Graph
Greedy Algorithm
Maximum Degree
ISSN:0104-6500, 1678-4804
Online-Zugang:Volltext
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Zusammenfassung:The Grundy index of a graph G =(V, E ) is the greatest number of colours that the greedy edge-colouring algorithm can use on G . We prove that the problem of determining the Grundy index of a graph G=(V, E ) is NP-hard for general graphs. We also show that this problem is polynomial-time solvable for caterpillars. More specifically, we prove that the Grundy index of a caterpillar is Δ ( G ) or Δ ( G )+1 and present a polynomial-time algorithm to determine it exactly.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0104-6500
1678-4804
DOI:10.1186/s13173-015-0036-x