Graphs and Bergman′s GK Gap Theorem
✍ Scribed by H.W. Ellingsen; D.R. Farkas
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 347 KB
- Volume
- 164
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
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## Abstract The minimum size of a __k__‐connected graph with given order and stability number is investigated. If no connectivity is required, the answer is given by Turán's Theorem. For connected graphs, the problem has been solved recently independently by Christophe et al., and by Gitler and Val
On the basis of the observation that a 3-regular graph has a perfect matching if and only if its line graph has a triangle-free 2 -factorisation, we show that a connected 4-regular graph has a triangle-free 2 -factorisation, provided it has no more than two cut-vertices belonging to a triangle. This