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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Bibliographic Details
Published in:Journal of the Brazilian Computer Society Vol. 21; no. 1; p. 1
Main Authors: Havet, Frédéric, Maia, A. Karolinna, Yu, Min-Li
Format: Journal Article
Language:English
Published: London Springer London 01.12.2015
Sociedade Brasileira de Computação
Springer Verlag
Subjects:
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 Access:Get full text
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Summary: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.
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ISSN:0104-6500
1678-4804
DOI:10.1186/s13173-015-0036-x