For every fixed integer k≥1, we prove that k-Edge Colouring is fixed-parameter-tractable when parameterized by the number of vertices of maximum degree.
@article{arxiv.1901.01861,
title = {On the Parameterized Complexity of $k$-Edge Colouring},
author = {Esther Galby and Paloma T. Lima and Daniël Paulusma and Bernard Ries},
journal= {arXiv preprint arXiv:1901.01861},
year = {2019}
}