Complexity of greedy edge-colouring - Havet, Frédéric; Maia, A. Karolinna; Yu, Min-Li (Journal of the Brazilian Computer Society, 2015)
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.