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
The chromatic index of nearly bipartite multigraphs
โ Scribed by Larry Eggan; Michael Plantholt
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 672 KB
- Volume
- 40
- Category
- Article
- ISSN
- 0095-8956
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๐ SIMILAR VOLUMES
We summarize previous results on the chromatic index of nearly complete simple graphs. Hilton has shown how the first of these results generalizes to multigraphs. We give an extension of another of the simple graph results to a multigraph version.
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
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