Complexity of greedy edge-colouring

Frédéric Havet 1 A Karolinna Maia 2 Min-Li Yu 3
1 COATI - Combinatorics, Optimization and Algorithms for Telecommunications
CRISAM - Inria Sophia Antipolis - Méditerranée , Laboratoire I3S - COMRED - COMmunications, Réseaux, systèmes Embarqués et Distribués
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 (G) or (G) + 1 and present a polynomial-time algorithm to determine it exactly.
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Frédéric Havet, A Karolinna Maia, Min-Li Yu. Complexity of greedy edge-colouring. Journal of the Brazilian Computer Society, Springer Verlag, 2015, 21 (18), ⟨10.1186/s13173-015-0036-x⟩. ⟨hal-01233312⟩

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