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# Applications of edge coloring of multigraphs to vertex coloring of graphs

@article{Kierstead1989ApplicationsOE, title={Applications of edge coloring of multigraphs to vertex coloring of graphs}, author={Hal A. Kierstead}, journal={Discrete Mathematics}, year={1989}, volume={74}, pages={117-124} }

- Published 1989 in Discrete Mathematics
DOI:10.1016/0012-365X(89)90203-3

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