Given a graph G and a positive integer k, denote by G[k] the graph obtained from G by replacing each vertex of G with an independent set of size k. A graph G is called pseudo-k Hamiltonian-connected if G[k] is Hamiltonian-connected, i.e., every two distinct vertices of G[k] are connected by a Hamiltonian path. A graph G is called pseudo Hamiltonian-connected if it is pseudo-k Hamiltonian-connec...

A Hamiltonian cycle is a closed path through all the vertices of a graph. Since discovering whether a graph has a Hamiltonian path or a Hamiltonian cycle are both NP-complete problems, researchers concentrated on formulating sufficient conditions that ensure Hamiltonicity of a graph. A Information Processing Letters 94(2005), 37-51] presents distance based sufficient conditions for the existenc...

PACS : 02.30.J, 11.10.E; MSC : 35L65, 35L70, 35Q35, 58F05, 58F07 keywords: Lagrangian, metrics of constant curvature, Hamiltonian structure, reciprocal transformation, Poisson brackets. Abstract. In this article we present a Lagrangian representation for evolutionary systems with a Hamiltonian structure determined by a differential-geometric Poisson bracket of the first order associated with me...

We show that a reversible non-Hamiltonian vector field at nonsemisimple 1:1 resonance can be split into a Hamiltonian and a non-Hamiltonian part in such a way that after reduction to the orbit space for the S1-action coming from the semisimple part of the linearized vector field the non-Hamiltonian part vanishes. As a consequence the reduced reversible vector field is Hamiltonian. We furthermor...

We say that a hypergraph H is hamiltonian path (cycle) saturated if H does not contain an open (closed) hamiltonian chain but by adding any new edge we create an open (closed) hamiltonian chain in H. In this paper we ask about the smallest size of an r-uniform hamiltonian path (cycle) saturated hypergraph, mainly for r = 3. We present a construction of a family of 3-uniform path (cycle) saturat...

We show that a reversible non-Hamiltonian vector field at nonsemisimple 1:1 resonance can be split into a Hamiltonian and a non-Hamiltonian part in such a way that after reduction to the orbit space for the Sl-action coming from the semisimple part of the linearized vector field the non-Hamiltonian part vanishes. As a consequence the reduced reversible vector field is Hamiltonian. We furthermor...

We consider the pair of graphs S and T such that every 3-connected {S, T}-free graph is hamiltonian connected. Such pairs are called hamiltonian connected pairs. We show three new hamiltonian connected pairs. Combing our results and a result of Shepherd, we conclude that if {S, T} is a pair of graphs such that every 2-connected {S, T}-free graph is hamiltonian then every 3-connected {S, T}-free...

We say that a hypergraph H is hamiltonian chain saturated if H does not contain a hamiltonian chain but by adding any new edge we create a hamiltonian chain in H. In this paper we ask about the smallest size of a k-uniform hamiltonian chain saturated hypergraph. We present a construction of a family of k-uniform hamiltonian chain saturated hypergraphs with O(nk−1/2) edges.

The perturbation theory for purely imaginary eigenvalues of Hamiltonian matrices under Hamiltonian and non-Hamiltonian perturbations is discussed. It is shown that there is a substantial difference in the behavior under these perturbations. The perturbation of real eigenvalues of real skew-Hamiltonian matrices under structured perturbations is discussed as well and these results are used to ana...