On Forbidden Pairs Implying Hamilton‐Connectedness
Jill R. Faudree, Ralph J. Faudree, Zdeněk Ryjáček, Petr Vrána · Journal of Graph Theory · 2012
Abstract 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.) [8] and (H. Broersma, R. J. Faudree, A. Huck, H. Trommel, and H. J. Veldman, J. Graph Theory, 40(2) (2002), 104–119.) [5]. 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.