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...

1. Model a producer/consumer system with two producers and three consumers. How can you modify this system to enforce a maximal capacity of ten simultaneous items in the channel? 2. An inhibitor arc between a place p and a transition t makes t firable only if the current marking at p is zero. In the following example, there is such an inhibitor arc between p1 and t. A marking (0, 2, 1) allows t...

1. Model a producer/consumer system with two producers and three consumers. How can you modify this system to enforce a maximal capacity of ten simultaneous items in the channel? 2. An inhibitor arc between a place p and a transition t makes t firable only if the current marking at p is zero. In the following example, there is such an inhibitor arc between p1 and t. A marking (0, 2, 1) allows t...

1. Introduction. In an earlier paper(2) by one of us, referred to hereafter as A.P.T., arc-preserving transformations were defined and studied in connection with an irreducibility condition on the transformation. It was shown, for example, that if A and B are compact locally connected metric continua which are cyclic (that is, without cut points) any single valued continuous arc-preserving and ...

Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3).

For a graph G of order n we consider the unique partition of its vertex set V (G) = A ∪ B with A = {v ∈ V (G) : d(v) ≥ n/2} and B = {v ∈ V (G) : d(v) < n/2}. Imposing conditions on the vertices of the set B we obtain new sufficient conditions for hamiltonian and pancyclic graphs.

A graph G of order n is said to be in the class O(n1) if deg(u)+deg(v)>n1 for every pair of nonadjacent vertices II, VE V(G). We characterise the graphs in O(n1) which are pancyclic.