On (Kq;k)-Stable Graphs
Article first published online: 15 OCT 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 74, Issue 2, pages 216–221, October 2013
How to Cite
Żak, A. (2013), On (Kq;k)-Stable Graphs. J. Graph Theory, 74: 216–221. doi: 10.1002/jgt.21705
- Issue published online: 2 AUG 2013
- Article first published online: 15 OCT 2012
- Manuscript Revised: 30 AUG 2012
- Manuscript Received: 2 JAN 2012
- Polish Ministry of Science and Higher Education
- complete graphs;
- vertex stability
A graph G is called -vertex stable if G contains a subgraph isomorphic to H even after removing any k of its vertices. By stab we denote the minimum size among the sizes of all -vertex stable graphs. Given an integer , we prove that, apart of some small values of k, stab. This confirms in the affirmative the conjecture of Dudek et al. [Discuss Math Graph Theory 28(1) (2008), 137–149]. Furthermore, we characterize the extremal graphs.