论文信息 - Edge-coloring of multigraphs: Recoloring technique

Edge-coloring of multigraphs: Recoloring technique

New upper and lower bounds for the chromatic index of a finite muitigraph are obtained. A complete description is given of multigraphs satisfying χ′ > 1/8(9ρ + 6) where χ′ and ρ denote the chromatic index and the maximum vertex degree of a multigraph. Some new and old conjectures are discussed.

Mark K. Goldberg | M. Goldberg

[1] Hian Poh Yap. A construction of chromatic index critical graphs , 1981, J. Graph Theory.

[2] J. C. Dunn,et al. A Fuzzy Relative of the ISODATA Process and Its Use in Detecting Compact Well-Separated Clusters , 1973 .

[3] R. Isaacs. Infinite Families of Nontrivial Trivalent Graphs Which are not Tait Colorable , 1975 .

[4] Ivan Tafteberg Jakobsen. Some remarks on the chromatic index of a graph , 1973 .

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

[6] Lowell W. Beineke,et al. On small graphs critical with respect to edge colourings , 1976, Discret. Math..

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

[8] Mark K. Goldberg,et al. Construction of class 2 graphs with maximum vertex degree 3 , 1981, J. Comb. Theory, Ser. B.

[9] Dominique de Werra,et al. Investigations on an edge coloring problem , 1971, Discret. Math..

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