Edge-Coloring Bipartite Multigraphs in O(E logD) Time

@article{Cole2001EdgeColoringBM,
  title={Edge-Coloring Bipartite Multigraphs in O(E logD) Time},
  author={Richard J. Cole and Kirstin Ost and Stefan Schirra},
  journal={Combinatorica},
  year={2001},
  volume={21},
  pages={5-12}
}
Let V, E, and D denote the cardinality of the vertex set, the cardinality of the edge set, and the maximum degree of a bipartite multigraph G. We show that a minimal edge-coloring of G can be computed in O(E logD time. This result follows from an algorithm for finding a matching in a regular bipartite graph in O(E) time. 

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