Bauer, D., Broersma, H. J., van den Heuvel, J., Kahl, N. and Schmeichel, E. (2013) Toughness and vertex degrees. Journal of Graph Theory, 72 (2). pp. 209-219. ISSN 0364-9024
Abstract
We study theorems giving sufficient conditions on the vertex degrees of a graph $G$ to guarantee $G$ is $t$-tough. We first give a best monotone theorem when $t\ge1$, but then show that for any integer $k\ge1$, a best monotone theorem for $t=\frac1k\le 1$ requires at least $f(k)\cdot|V(G)|$ nonredundant conditions, where $f(k)$ grows superpolynomially as $k\rightarrow\infty$. When $t<1$, we give an additional, simple theorem for $G$ to be $t$-tough, in terms of its vertex degrees.
| Item Type: | Article |
|---|---|
| Official URL: | http://onlinelibrary.wiley.com/ |
| Additional Information: | © 2013 John Wiley & Sons, Inc. |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Identification Number: | degree sequences; toughness; best monotone theorem |
| Funders: | Engineering and Physical Sciences Research Council |
| Projects: | EP/F064551/1 |
| Date Deposited: | 09 Apr 2010 13:16 |
| URL: | http://eprints.lse.ac.uk/27680/ |
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