Contract grant sponsor: EPSRC; Contract grant number: EP/F064551/1; Contract grant sponsor: RFBR; Contract numbers: 12-01-00090, 12-01-00093, 12-01-00184, and 12-01-33028; Contract grant sponsor: Ministry of Education and Science of the Russian Federation; Contract grant number: 14.740.11.0868.
On Toughness and Hamiltonicity of 2K2-Free Graphs
Article first published online: 19 FEB 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 75, Issue 3, pages 244–255, March 2014
How to Cite
Broersma, H., Patel, V. and Pyatkin, A. (2014), On Toughness and Hamiltonicity of 2K2-Free Graphs. J. Graph Theory, 75: 244–255. doi: 10.1002/jgt.21734
- Issue published online: 6 JAN 2014
- Article first published online: 19 FEB 2013
- Manuscript Revised: 15 JAN 2013
- Manuscript Received: 4 AUG 2011
- EPSRC. Grant Number: EP/F064551/1
- RFBR. Grant Numbers: 12-01-00090, 12-01-00093, 12-01-00184, 12-01-33028
- Ministry of education and science of the Russian Federation. Grant Number: 14.740.11.0868
- 2K2-free graphs;
- split graphs;
- Hamilton cycle
The toughness of a (noncomplete) graph G is the minimum value of t for which there is a vertex cut A whose removal yields components. Determining toughness is an NP-hard problem for general input graphs. The toughness conjecture of Chvátal, which states that there exists a constant t such that every graph on at least three vertices with toughness at least t is hamiltonian, is still open for general graphs. We extend some known toughness results for split graphs to the more general class of 2K2-free graphs, that is, graphs that do not contain two vertex-disjoint edges as an induced subgraph. We prove that the problem of determining toughness is polynomially solvable and that Chvátal's toughness conjecture is true for 2K2-free graphs.