This paper introduces a complete description of constructing a Hamiltonian cycle in the Extended OTIS-n-Cube topology. The recently proposed network has many good topological features such as regular degree, semantic structure, low diameter, and ability to embed graphs and cycles. Constructing a Hamiltonian cycle is an important feature for any topology due to the importance of broadcast messag...

For arbitrary undirected graph G, we are designing SATISFIABILITY problem (SAT) for HCP, using tools of Boolean algebra only. The obtained SAT be the logic formulation of conditions for Hamiltonian cycle existence, and use m Boolean variables, where m is the number of graph edges. This Boolean expression is true if and only if an initial graph is Hamiltonian. That is, each satisfying assignment...

We give sufficient Ore-type conditions for a balanced bipartite graph to contain every matching in a hamiltonian cycle or a cycle not necessarily hamiltonian. Moreover, for the hamiltonian case we prove that the condition is almost best possible. © 2006 Elsevier B.V. All rights reserved.

The Hamiltonian Cycle problem asks if an n-vertex graph G has a cycle passing through all vertices of G. This problem is a classic NP-complete problem. So far, finding an exact algorithm that solves it in O∗(αn) time for some constant α < 2 is a notorious open problem. For a claw-free graph G, finding a hamiltonian cycle is equivalent to finding a closed trail (eulerian subgraph) that dominates...

We propose a new method to provide network survivability using the Restricted P-Cycle by Hamiltonian cycle (RPC), which is the improved version of p-cycle. Because p-cycle has some problem files, it is not applied to dynamic traffic or varying QoS in real time circumstance. However, RPC can significantly reduce complexity in finding proper patterns restricted by Hamiltonian cycle, which has min...

The Hamiltonian cycle problem is one of the most popular NP-complete problems, and remains NP-complete even if we restrict ourselves to a class of (3-connected cubic) planar graphs [5,9]. Therefore, there seems to be no polynomial-time algorithm for the Hamiltonian cycle problem. However, for certain (nontrivial) classes of restricted graphs, there exist polynomial-time algorithms [3,4,6]. In f...

Many hard graph problems, such as Hamiltonian Cycle, become FPT when parameterized by treewidth, a parameter that is bounded only on sparse graphs. When parameterized by the more general parameter cliquewidth, Hamiltonian Cycle becomes W[1]-hard, as shown by Fomin et al. [5]. Sæther and Telle address this problem in their paper [13] by introducing a new parameter, split-matching-width, which li...

Ng and Schultz [J Graph Theory 1 (1997), 45±57] introduced the idea of cycle orderability. For a positive integer k, a graph G is k-ordered if for every ordered sequence of k vertices, there is a cycle that encounters the vertices of the sequence in the given order. If the cycle is also a Hamiltonian cycle, then G is said to be k-ordered Hamiltonian. We give sum of degree conditions for nonadja...

It is important for a network to tolerate as many faults as possible. With the graph representation of an interconnection network, a k-regular hamiltonian and hamiltonian connected network is super fault-tolerant hamiltonian if it remains hamiltonian after removing up to k 2 vertices and/or edges and remains hamiltonian connected after removing up to k 3 vertices and/or edges. Super fault-toler...

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.