✦ LIBER ✦

Approximating the chromatic index of multigraphs

✍ Scribed by Guantao Chen; Xingxing Yu; Wenan Zang

Publisher: Springer US
Year: 2009
Tongue: English
Weight: 654 KB
Volume: 21
Category: Article
ISSN: 1382-6905
DOI: 10.1007/s10878-009-9232-y

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

Asymptotics of the Chromatic Index for M

Asymptotics of the Chromatic Index for Multigraphs

✍ Jeff Kahn 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 835 KB

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

The chromatic index of nearly bipartite

The chromatic index of nearly bipartite multigraphs

✍ Larry Eggan; Michael Plantholt 📂 Article 📅 1986 🏛 Elsevier Science 🌐 English ⚖ 672 KB

Asymptotics of the list-chromatic index

Asymptotics of the list-chromatic index for multigraphs

✍ Jeff Kahn 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 272 KB 👁 1 views

A note concerning the chromatic index of

A note concerning the chromatic index of multigraphs

✍ A. J. W. Hilton; Bill Jackson 📂 Article 📅 1987 🏛 John Wiley and Sons 🌐 English ⚖ 214 KB

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

Chromatic-index critical multigraphs of

Chromatic-index critical multigraphs of order 20

✍ Gr�newald, Stefan 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 243 KB 👁 1 views

The weak critical graph conjecture [1,7] claims that there exists a constant c > 0 such that every critical multigraph M with at most c • ∆(M ) vertices has odd order. We disprove this conjecture by constructing critical multigraphs of order 20 with maximum degree k for all k ≥ 5.

The List Chromatic Index of a Bipartite

The List Chromatic Index of a Bipartite Multigraph

✍ F. Galvin 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 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