Bipartite Edge Coloring in O(Delta m) Time

@article{Schrijver1998BipartiteEC,
  title={Bipartite Edge Coloring in O(Delta m) Time},
  author={Alexander Schrijver},
  journal={SIAM J. Comput.},
  year={1998},
  volume={28},
  pages={841-846}
}
We show that a minimum edge coloring of a bipartite graph can be found in O(∆m) time, where ∆ and m denote the maximum degree and the number of edges of G, respectively. It is equivalent to finding a perfect matching in a k-regular bipartite graph in O(km) time. By sharpening the methods, a minimum edge coloring of a bipartite graph can be found in O((pmax(∆) + log ∆)m) time, where pmax(∆) is the largest prime factor of ∆. Moreover, a perfect matching in a k-regular bipartite graph can be found… CONTINUE READING
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