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

In this paper we present a characterization of connected graphs of order 2n with domination numbern. Using this class of graphs, we determine an infinite class of graphs with the property that the… Expand

In 1963, Moon and Moser gave a bipartite analogue to Ore's famed theorem on hamiltonian graphs, consisting of one infinite family and two exceptional graphs of order eight.Expand

Let $G$ be a fixed graph and let ${\mathcal F}$ be a family of graphs. A subgraph $J$ of $G$ is ${\mathcal F}$-saturated if no member of ${\mathcal F}$ is a subgraph of $J$, but for any edge $e$ in… 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