… In this paper, two necessary and sufficient conditions for a general graph and a bipartite
graph being F-Hamiltonian are provided, respectively. @ 1999 Elsevier Science BV All …

… With each nonempty graph G one can associate a graph L(G), called the line graph of G,
with … This implies that L(G) is not f-Hamiltonian and hence &(G) 3 2. We conclude this section …

… (i) If G satisfies uz 1 n + 1, then G is F-hamiltonian. (ii) If G satisfies u2 1 n - 1, then G is F-…
generalized degree approach) in relation to F-hamiltonian graphs. The reader interested in this …

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 …

… We use f-Hamiltonian to denote this property of G. Similarly, we use f-Hamiltonian connected
to denote the property that there is a Hamiltonian path between any two vertices in G Ą F for …

… The kth power of C is the graph obtained from C by joining every pair of vertices at a distance
at most k in C. Let G be a graph on n 2 3 vertices. A classical result of Dirac [3] asserts that …

… We use Kmfor the complete graph on m vertices. The vertex set of a graph G is denoted by
V(… The proof of the theorem is by induction on the number of vertices ofthe graphs. We choose …

… A burnt pancake graph is one such topology. In this paper, we prove that a faulty burnt
pancake graph with degree n has a fault-free Hamiltonian cycle if the number of the faulty …

… Suppose G is a graph, F is a 1-factor of G. G is called F-Hamiltonian, if there exists a
Hamiltonian cycle containing F in G. In this paper, two necessary and sufficient conditions …