On Forbidden Pairs Implying Hamilton-Connectedness
Version of Record online: 18 MAY 2012
© 2012 Wiley Periodicals, Inc.
Journal of Graph Theory
Volume 72, Issue 3, pages 327–345, March 2013
How to Cite
Faudree, J. R., Faudree, R. J., Ryjáček, Z. and Vrána, P. (2013), On Forbidden Pairs Implying Hamilton-Connectedness. J. Graph Theory, 72: 327–345. doi: 10.1002/jgt.21645
- Issue online: 23 JAN 2013
- Version of Record online: 18 MAY 2012
- Manuscript Revised: 14 DEC 2011
- Manuscript Received: 4 MAR 2010
- forbidden subgraphs;
- hamilton connected
Let X, Y be connected graphs. A graph G is -free if G contains a copy of neither X nor Y as an induced subgraph. Pairs of connected graphs such that every 3-connected -free graph is Hamilton connected have been investigated most recently in (Guantao Chen and Ronald J. Gould, Bull. Inst. Combin. Appl., 29 (2000), 25–32.)  and (H. Broersma, R. J. Faudree, A. Huck, H. Trommel, and H. J. Veldman, J. Graph Theory, 40(2) (2002), 104–119.) . This paper improves those results. Specifically, it is shown that every 3-connected -free graph is Hamilton connected for and or N1, 2, 2 and the proof of this result uses a new closure technique developed by the third and fourth authors. A discussion of restrictions on the nature of the graph Y is also included.