On Forbidden Pairs Implying Hamilton-Connectedness

Let X, Y be connected graphs. A graph G is (X, Y )-free if G contains a copy of neither X nor Y as an induced subgraph. Pairs of connected graphs X, Y such that every 3-connected (X, Y )-free graph is Hamilton connected have been investigated most recently in [8] and [5]. This paper improves those results. Specifically, it is shown that every 3-connected (X, Y )-free graph is Hamilton connected for X = K1,3 and Y = P8, N1,1,3, 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.