## Abstract In this article, we prove the following theorem. Let __k__ ≥ 3 be an integer, __G__ be a __k__‐connected graph with minimum degree __d__ and __X__ be a set of __k__ + 1 vertices on a cycle. Then __G__ has a cycle of length at least min {2d,|V(G)|} passing through __X__. This result give
✦ LIBER ✦
Circuits through prescribed vertices in k-connected k-regular graphs
✍ Scribed by Roland Häggkvist; Wolfgang Mader
- Publisher
- John Wiley and Sons
- Year
- 2002
- Tongue
- English
- Weight
- 178 KB
- Volume
- 39
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We show that every set of $k+\lfloor{1\over 3}\sqrt{k}\rfloor$ vertices in a k‐connected k‐regular graph belongs to some circuit. © 2002 John Wiley & Sons, Inc. J Graph Theory 39: 145–163, 2002
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