✦ LIBER ✦

A Note on List Arboricity

✍ Scribed by P.D. Seymour

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 181 KB
Volume: 72
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1997.1784

No coin nor oath required. For personal study only.

✦ Synopsis

We show that, for any graph or matroid, its arboricity'' and its list arboricity'' are equal.

1998 Academic Press

A celebrated recent theorem of Galvin [2] asserts that for any bipartite graph, its chromatic index and its list-chromatic index are equal. This can be formulated as a property of the ``independence system'' of matchings in a bipartite graph. In private communication, Stefan Burr asked which other independence systems had this property, and in particular whether the independence system of forests in a graph had the property. We shall show that the latter is true. More precisely, we prove the following.

Proof. We may assume that P(e) [1, ..., n] for all e # E(M). For 1 i n, let Q i =[e # E(M) : i # P(e)]. Let M i be the restriction of M to Q i

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