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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Vydané v:	Journal of the Brazilian Computer Society Ročník 21; číslo 1; s. 1
Hlavní autori:	Havet, Frédéric, Maia, A. Karolinna, Yu, Min-Li
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	London Springer London 01.12.2015 Sociedade Brasileira de Computação Springer Verlag
Predmet:	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
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Shrnutí:	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.
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	0104-6500 1678-4804
DOI:	10.1186/s13173-015-0036-x