An implicit degree condition for hamiltonian cycles in k-connected graphs;

An implicit degree condition for Hamiltonian cycles in k-connected claw-free graphs;

We will provide some formulas for calculating the number of all distinct hamiltonian cycles in some simple graphs , we will also discuss upper (resp.

According to the analysis of the solution to Knight s Tour Problem given by Euler and the knowledge of Hamilton path and Hamilton cycle,we obtain that the solution denotes a Hamilton cycle in the defined bigraph.

The paper utilizes the matrix turning to realize that using the principle of one by one revision of two sides to obtain the best Hamilton Circle.

We will present eight sufficient conditions for the existence of hamiltonian cycles in A1,r-free graphs by studying the essential independent sets in a graph and the independent sets in its partially square graph.

Chapter 1 is intended as a firstintroduction to basic concepts and terminations of graphs, together with the backgroundon Hamilton cycle of graphs.

Time dependent traveling salesman problem(TDTSP)is an extension of the traveling salesman problem(TSP),in which the travel time or cost between two nodes depends on not only the distance between the nodes,but also the time of day or the node position in the Hamilton cycle.

For any n-dimensional(n≥3) folded hypercube with at most 2n-3 faulty edges in which each vertex is incident with at least two fault-free edges,it is proved that there exists a fault-free Hamiltonian cycle.

As consequences, we obtain the degree conditions for a graph with a Hamiltonian cycle C to have a [a ,b] - factor Fsuch that E(C)(?)E(F

If one network contains Hamiltonian cycles (Hamiltonian paths) and cycles of variable lengths, then it can effectively simulate the algorithms designed based on rings and linear arrays.