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The 3-connected graphs having a longest cycle containing only three contractible edges

✍ Scribed by R. E. L. Aldred; Robert L. Hemminger; Katsuhiro Ota

Publisher
John Wiley and Sons
Year
1993
Tongue
English
Weight
570 KB
Volume
17
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

It is shown that with one small exception, the 3‐connected graphs admitting longest cycles that contain less than four contractible edges of the parent graph are the members of three closely related infinite families. © 1993 John Wiley & Sons, Inc.

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Longest cycles in 3-connected graphs contain three contractible edges
✍ Nathaniel Dean; Robert L. Hemminger; Katsuhiro Ota 📂 Article 📅 1989 🏛 John Wiley and Sons 🌐 English ⚖ 221 KB 👁 1 views

We show that if G is a 3-connected graph of order at least seven, then every longest path between distinct vertices in G contains at least two contractible edges. An immediate corollary is that longest cycles in such graphs contain at least three contractible edges. We consider only finite undirect