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Reports (Research Report) Year : 2012

Complexity of greedy edge-colouring

Abstract

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 $\Delta(G)$ or $\Delta(G)+1$ and present a polynomial-time algorithm to determine it exactly.
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Dates and versions

hal-00762534 , version 1 (07-12-2012)

Identifiers

  • HAL Id : hal-00762534 , version 1

Cite

Frédéric Havet, Ana Karolinna Maia de Oliviera, Min-Li Yu. Complexity of greedy edge-colouring. [Research Report] RR-8171, INRIA. 2012, pp.13. ⟨hal-00762534⟩
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