n-Hamiltonian graphs

KNESER GRAPHS ARE HAMILTONIAN FOR n

Hamiltonian cycles in n-factor-critical graphs

A graph G is said to be n-factor-critical if G − S has a 1-factor for any S ⊂V (G) with |S| = n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with 3(G)¿ 2 (p−n−1), then G is hamiltonian with some exceptions. To extend this theorem, we de6ne a (k; n)-factor-critical graph to be a graph G such that G − S has a k-factor for any S ⊂V (G) with |S| = n. We con...

Hamiltonian Factors in Hamiltonian Graphs

Let G be a Hamiltonian graph. A factor F of G is called a Hamiltonian factor if F contains a Hamiltonian cycle. In this paper, two sufficient conditions are given, which are two neighborhood conditions for a Hamiltonian graph G to have a Hamiltonian factor. Keywords—graph, neighborhood, factor, Hamiltonian factor.

$n$-Array Jacobson graphs

We generalize the notion of Jacobson graphs into $n$-array columns called $n$-array Jacobson graphs and determine their connectivities and diameters. Also, we will study forbidden structures of these graphs and determine when an $n$-array Jacobson graph is planar, outer planar, projective, perfect or domination perfect.

Hamiltonian N∑

Random s = 1/2 XY chains and the theory of quasi-one-dimensional ferroelectrics with hydrogen bonds L'viv-1994