Supported by EPSRC grant EP/F064551/1.
Toughness and Vertex Degrees
Article first published online: 24 JUL 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 72, Issue 2, pages 209–219, February 2013
How to Cite
Bauer, D., Broersma, H. J., van den Heuvel, J., Kahl, N. and Schmeichel, E. (2013), Toughness and Vertex Degrees. J. Graph Theory, 72: 209–219. doi: 10.1002/jgt.21639
- Issue published online: 9 JAN 2013
- Article first published online: 24 JUL 2012
- Manuscript Revised: 3 NOV 2011
- Manuscript Received: 14 JAN 2010
- degree sequences;
- best monotone theorem
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 , but then show that for any integer , a best monotone theorem for requires at least nonredundant conditions, where grows superpolynomially as . When , we give an additional, simple theorem for G to be t-tough, in terms of its vertex degrees.