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Nearly light cycles in embedded graphs and crossing-critical graphs

✍ Scribed by Mario Lomelí; Gelasio Salazar

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 101 KB
Volume: 53
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20172

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✦ Synopsis

Abstract

We find a lower bound for the proportion of face boundaries of an embedded graph that are nearly light (that is, they have bounded length and at most one vertex of large degree). As an application, we show that every sufficiently large k‐crossing‐critical graph has crossing number at most 2__k__ + 23. © 2006 Wiley Periodicals, Inc. J Graph Theory 53: 151–156, 2006

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