On 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...

On Hamiltonian Regular Graphs

In this paper we shall determine, when 1 = 6, bounds for numbers f(k, I) and F{k, 1) defined as follows: f{k, l)/F(k, I) is defined to be the smallest integer n for which there exists a regular graph/Hamiltonian regular graph of valency k and girth I having n vertices. The problem of determining minimal regular graphs of given girth was first considered by Tutte [9]. Bounds for f(k, I) have bee...

On hamiltonian Toeplitz graphs

In this paper we will consider hamiltonian properties of so-called Toeplitz graphs, which are defined as follows: Definition 1 Let n,m, a1, . . . , am ∈ N, 0 < a1 < · · · < am < n and V := {0, . . . , n− 1}. Define E := {[i, j] ∈ V 2 : ∃k ∈ {1, . . . , m} : |j − i| = ak}. Then the graph (V,E) with set of vertices V and set of edges E is called an undirected Toeplitz graph with entries (or strip...

On pancyclism in hamiltonian graphs

We investigate the set of cycle lengths occurring in a hamiltonian graph with at least one or two vertices of large degree. We prove that in every case this set contains all the integers between 3 and some t, where t depends on the order of the graph and the degrees of vertices. c © 2002 Elsevier Science B.V. All rights reserved.