Contract grant sponsor: NSF: contract grant numbers: IIS-1117631 and DMS-1001091.
Simplicial Vertices in Graphs with no Induced Four-Edge Path or Four-Edge Antipath, and the H6-Conjecture
Version of Record online: 27 AUG 2013
© 2013 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 76, Issue 4, pages 249–261, August 2014
How to Cite
Chudnovsky, M. and Maceli, P. (2014), Simplicial Vertices in Graphs with no Induced Four-Edge Path or Four-Edge Antipath, and the H6-Conjecture. J. Graph Theory, 76: 249–261. doi: 10.1002/jgt.21763
- Issue online: 3 JUN 2014
- Version of Record online: 27 AUG 2013
- Manuscript Revised: 27 MAY 2013
- Manuscript Received: 16 OCT 2012
- NSF. Grant Numbers: IIS-1117631, DMS-1001091
- induced subgraph;
Let be the class of all graphs with no induced four-edge path or four-edge antipath. Hayward and Nastos  conjectured that every prime graph in not isomorphic to the cycle of length five is either a split graph or contains a certain useful arrangement of simplicial and antisimplicial vertices. In this article, we give a counterexample to their conjecture, and prove a slightly weaker version. Additionally, applying a result of the first author and Seymour  we give a short proof of Fouquet's result  on the structure of the subclass of bull-free graphs contained in .