The square of a graph is obtained by adding additional edges joining all pair of vertices of distance two in the original graph. Particularly, if C is a hamiltonian cycle of a graph G, then the square of C is called a hamiltonian square of G. In this paper, we characterize all possible forbidden pairs, which implies the containment of a hamiltonian square, in a 4-connected graph. The connectivi...

For an arbitrary undirected graph G, we are designing a logical model for the Hamiltonian Cycle Problem (HCP), using tools of Boolean algebra only. The obtained model is a logic formulation of the conditions for the existence of the Hamiltonian cycle, and uses m Boolean variables, where m is the number of the edges of a graph. This Boolean expression is true if and only if an initial graph is H...

Using the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph, we continue the investigation of the existence of a decomposition of the complete 3-uniform hypergraph into Hamiltonian cycles began by Bailey and Stevens. We also discuss two extensions of the problem: to the complete 3-uniform hypergraph from which a parallel class of triples has been removed, and to the com...

We first show that if a graph G of order n contains a hamiltonian path connecting two nonadjacent vertices u and v such that d(u) + d(v) ≥ n, then G is pancyclic. By using this result, we prove that if G is hamiltonian with order n ≥ 20 and if G has two nonadjacent vertices u and v such that d(u) + d(v) ≥ n + z, where z = 0 when n is odd and z = 1 otherwise, then G contains a cycle of length m ...

We study portfolios of parallel strategies for Boolean Satisfiability (SAT) based solving of Hamiltonian Cycle Problems (HCPs). The strategies are based on our techniques for relative SAT encoding of permutations with constraints, and exploit: 1) encodings that eliminate half of the ordering Boolean variables and two-thirds of the transitivity constraints; 2) 12 triangulation heuristics for min...

in this research we work with the effective hamiltonian and the quark model. we investigate the decay rates of matter-antimatter of quark. we describe the effective hamiltonian theory and apply this theory to the calculation of current-current ( ), qcd penguin ( ), magnetic dipole ( ) and electroweak penguin ( ) decay rates. the gluonic penguin structure of hadronic decays is studied through th...

1. INTRODUCTION. A Hamiltonian cycle in a graph is a path in the graph which visits each vertex exactly once and returns to the starting vertex. Let í µí°¾ í µí±› be a weighted complete graph with í µí±› vertices. We define the weight of an edge as the square of the distance between two end points of the edge. The weight of a path í µí±ƒ is the sum of the weights of all edges in the path and de...

Shape matching plays important roles in many fields such as object recognition, image retrieval etc. Belongie, et al. recently proposed a novel shape matching algorithm utilizing the shape context as a shape descriptor and the magnitude of the aligning two shape contexts as a distance measure. It was claimed to be an information rich descriptor that is invariant to translation, scale, and rotat...

Frieze [1] introduced a heuristic polynomial-time algorithm, Ham, for finding Hamiltonian cycles in random graphs with high probability. We wanted to see how this algorithm performs in practice, and whether it could be improved by modifying it. For this purpose, we borrowed an idea from an algorithm by Keydar called SemiHam [2]. SemiHam is a modification of Ham that finds Hamiltonian cycles in ...

A cycle C in a graph G is extendible if there exists a cycle C 0 in G such that V (C) V (C 0) and jV (C 0)j = jV (C)j + 1. A graph G is cycle extendible if G contains at least one cycle and every nonhamiltonian cycle in G is extendible. A graph G is fully cycle extendible if G is cycle extendible and every vertex lies on a 3-cycle of G. G. Hendry asked if every hamiltonian chordal graph is full...