This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains material on closely related topics such as traceable, pancyclic and hamiltonian-connected graphs and digraphs.

Jackson and Ordaz conjectured that if the stability number (G) of a graph G is no greater than its connectivity (G) then G is pancyclic. Applying Ramsey’s theorem we prove the pancyclicity of every graph G with (G) su7ciently large with respect to (G). c © 2003 Elsevier B.V. All rights reserved. MSC: 05C38; 05C45

In this note, we consider the i-block intersection graphs (i-BIG) of a universal-friend friendship 3-hypergraph and show that they are pancyclic for i = 1, 2. We also show that the 1-BIG of a universalfriend friendship 3-hypergraph is Hamiltonian-connected.

We prove that every 2{connected K 1;3-free and Z 3 ?free graph is hamiltonian except for two graphs. Furthermore, we give a complete characterization of all 2?connected, K 1;3-free graphs, which are not pancyclic, and which are Z 3-free, B-free, W-free, or HP 7 ?free.

This article is intended as a survey, updating earlier surveys in the area. For completeness of the presentation of both particular questions and the general area, it also contains some material on closely related topics such as traceable, pancyclic and Hamiltonian connected graphs.

In this paper we characterize those pairs of forbidden subgraphs sufficient to imply various hamiltonian type properties in graphs. In particular, we find all forbidden pairs sufficient, along with a minor connectivity condition, to imply a graph is traceable, hamiltonian, pancyclic, panconnected or cycle extendable. We also consider the case of hamiltonian-connected graphs and present a result...