论文信息 - Regular Multigraphs of High Degree are 1‐Factorizable

Regular Multigraphs of High Degree are 1‐Factorizable

Chetwynd and Hilton showed that any regular simple graph with even order n and maximum degree at least \n has chromatic index equal to its maximum degree. We show how to extend this result to general multigraphs, including those of odd order. This also verifies a special case of conjectures by Goldberg and Seymour.

Shailesh K. Tipnis | Michael J. Plantholt

[1] Ina Ruck,et al. USA , 1969, The Lancet.

[2] Takao Nishizeki,et al. An upper bound on the chromatic index of multigraphs , 1985 .

[3] P. D. Seymour,et al. On Multi‐Colourings of Cubic Graphs, and Conjectures of Fulkerson and Tutte , 1979 .

[4] Odile Marcotte,et al. On the Chromatic Index of Multigraphs and a Conjecture of Seymour, (II) , 1990, Polyhedral Combinatorics.

[5] V. G. Vizing. The chromatic class of a multigraph , 1965 .

[6] A. Hilton,et al. Regular Graphs of High Degree are 1‐Factorizable , 1985 .

[7] Anthony J. W. Hilton,et al. 1-factorizing Regular Graphs of High Degree - an Improved Bound , 1989, Discret. Math..

[8] Odile Marcotte. On the chromatic index of multigraphs and a conjecture of Seymour (I) , 1986, J. Comb. Theory, Ser. B.

[9] C. Shannon. A Theorem on Coloring the Lines of a Network , 1949 .

[10] Mark K. Goldberg,et al. Edge-coloring of multigraphs: Recoloring technique , 1984, J. Graph Theory.

[11] G. Dirac. Some Theorems on Abstract Graphs , 1952 .