✦ LIBER ✦

Handbook of Graph Theoryby Jonathan L. Gross; Jay Yellen

✍ Scribed by Review by: Robert A. Beezer

Book ID: 124944351
Publisher: Society for Industrial and Applied Mathematics
Year: 2006
Tongue: English
Weight: 322 KB
Volume: 48
Category: Article
ISSN: 0036-1445
DOI: 10.2307/20453760

No coin nor oath required. For personal study only.

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It is proved that every connected simplicial graph with minimum valence at least three has maximum genus at least one-quarter of its cycle rank. This follows from the technical result that every 3-regular simplicial graph except K4 has a Xuong co-tree whose odd components have only one edge each. It