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}
}
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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References

Publications referenced by this paper.
Showing 1-7 of 7 references

On edge colorings

  • L. D. Andersen
  • graphs, Math. Stand
  • 1977

A theorem on coloring the lines of a network

  • C. E. Shannon
  • J. Math. Phys
  • 1949

Kierstead , On the chromatic index of multigraphs without large triangles

  • A. H.
  • J . Graph Theory

On coloring nodes of a network

  • R. L. Brooks
  • Proc . Cambridge Phil . Sot .

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