We characterize those pairs of forbidden subgraphs sufficient to imply various hamiltonian type properties in graphs and present a result concerning the pairs for such graphs.Expand

We investigate the relationship between the cardinality of the union of the neighborhoods of an arbitrary pair of nonadjacent vertices and various hamiltonian type properties in graphs. We show that if G is 2-connected, of order p ≥ 3 and if N(x) ⌣ N(y)∥ ≧ (p − 1)2, then G is traceable.Expand

For a finite nonempty set of integers, each of which is at least two, and an integern ≥ 3, the numberf(;n) is defined as the least order of a graph having degree set and girthn. The numberf(;n) is… Expand

Given a family of graphs F , a graph G is F-saturated if no element of F is a subgraph of G, but for any edge e in G, some element of F is a subgraph of G + e. Let sat(n,F) denote the minimum number… Expand

A graph $G$ is said to be F -saturated if G contains no copy of F as a subgraph, but for any edge in the complement of $G$, the graph does contain a cycle of length $l$.Expand

We consider the problem of finding the minimum number n such that any k edge colored complete graph on n vertices contains either a three colored triangle or a monochromatic copy of the graph G.Expand

We say a graph G is H-linked if for every choice of k vertices v1, . . . , vk in G, there exists a subdivision of H in G such that vi represents hi (for all i).Expand