Applications of edge coloring of multigraphs to vertex coloring of graphs

  title={Applications of edge coloring of multigraphs to vertex coloring of graphs},
  author={Hal A. Kierstead},
  journal={Discrete Mathematics},
Perhaps the two most important results on edge coloring are Vizing’s Theorem [16], which states that the chromatic index x’(M) of a multigraph 1w with maximum degree A(M) and maximum multiplicity p(M) satisfies A(M) =Z x’(M) s A(-M) + cc(M), and Holyer’s Theorem [g], which states that the problem of determining the chromatic index of even a simple graph is NP-complete. In some sense these two results solve the edge coloring problem for simple graphs. However, the upper bound is quite loose for… CONTINUE READING


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