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The chromatic class of a multigraph

โœ Scribed by V. G. Vizing

Publisher
Springer US
Year
1965
Tongue
English
Weight
857 KB
Volume
1
Category
Article
ISSN
1573-8337

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๐Ÿ“œ SIMILAR VOLUMES

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โœ F. Galvin ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 243 KB

For a bipartite multigraph, the list chromatic index is equal to the chromatic index (which is, of course, the same as the maximum degree). This generalizes Janssen's result on complete bipartite graphs \(K_{m, n}\) with \(m \neq n\); in the case of \(K_{n, n}\) it answers a question of Dinitz. (The

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We consider colorings of the directed and undirected edges of a mixed multigraph G by an ordered set of colors. We color each undirected edge in one color and each directed edge in two colors, such that the color of the first half of a directed edge is smaller than the color of the second half. The

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We improve an upper bound for the chromatic index of a multigraph due to Andersen and Gol'dberg. As a corollary w e deduce that if no t w o edges of multiplicity at least t w o in G are adjacent, then ,y'(G) s A ( G ) + 1. In addition w e generalize results concerning the structure of critical graph

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For a multigraph G, let D(G) denote maximum degree and set We show that the chromatic index /$(G) is asymptotically max[D(G), 1(G)]. The latter is, by a theorem of Edmonds (1965), the fractional chromatic index of G, and the asymptotics established here are part of a conjecture of the author predic