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On removable cycles through every edge

✍ Scribed by Manoel Lemos; James Oxley

Publisher: John Wiley and Sons
Year: 2003
Tongue: English
Weight: 102 KB
Volume: 42
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.10082

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✦ Synopsis

Abstract

Mader and Jackson independently proved that every 2‐connected simple graph G with minimum degree at least four has a removable cycle, that is, a cycle C such that G/E(C) is 2‐connected. This paper considers the problem of determining when every edge of a 2‐connected graph G, simple or not, can be guaranteed to lie in some removable cycle. The main result establishes that if every deletion of two edges from G remains 2‐connected, then, not only is every edge in a removable cycle but, for every two edges, there are edge‐disjoint removable cycles such that each contains one of the distinguished edges. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 155–164, 2003

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