Two Sufficient Conditions for Graphs to Be Traceable or 1-Hamiltonian;

A Sufficient Condition for Hamilton K_1,m-free Graphs;

For a simple graph G=(V,E),Ore theorem states that G is Hamiltonian if every pair of nonadjacent vertices u and v satisfies d(u)+d(v)≥|V|.

If a connected graph G is 1-hamiltonian(contains a 2factor with k(k2) cycles、is vertexpancyclic ordered、contains two edge-disjoint hamiltonian cycles、is panconnected),then L(G) also is1-hamiltonian(contains a 2-factor with k(k2) cycles、is vertexpancyclic ordered、contains two edge-disjoint hamiltonian cycles、is panconnected).

By using Hamilton graph,the problem of wagons placing-in and taking-out on branch-shaped sidings can be turned into searching Hamilton loop of minimum power.

he concept of the degree of a face is introduced, associated theoreme as necessary conditions of Hamilton graph are presented, and a method to search for Hamilton circuits in a given connected planer graphabsorbing transformation of graph-is Put forward.

By adopting Hamilton Graph, the paper builds up a mathematical model for wagons’ placing-in and taking-out and goods loading & unloading operation.

Moreover, the conjecture in the case of a block with cyclomatic number 2 is confirmed by constructing a Hamilton cycle.

Hamiltonicity,neighborhood union and square graphs of claw-free graphs;

Degree Sum of Independent Sets and Hamiltonicity of Graphs;

It is well-known that the problem on hamiltonicity of graphs is a very important problem in graph theory and the research is very active.