An approximate König's theorem for edge-coloring weighted bipartite graphs

@inproceedings{Correa2004AnAK,
  title={An approximate K{\"o}nig's theorem for edge-coloring weighted bipartite graphs},
  author={J. Correa and M. Goemans},
  booktitle={STOC '04},
  year={2004}
}
We consider a generalization of edge coloring bipartite graphs in which every edge has a weight in [0,1] and the coloring of the edges must satisfy that the sum of the weights of the edges incident to a vertex v of any color must be at most 1. For unit weights, König's theorem says that the number of colors needed is exactly the maximum degree. For this generalization, we show that 2. 557 n + o(n) colors are sufficient where n is the maximum total weight adjacent to any vertex, improving the… Expand
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