【摘要】 利用图论的基本方法及其思想,结合相关定义、定理提出了两个严格有向图含有向Hamilton路的两个充分条件,即D为具有n(≥2)个顶点的严格强连通有向图:1)如果对任意具有共同的内邻点或者具有共同的外邻点的非邻接顶点对{x,y},都有d(x)+d(y)≥2n+1,且min{d+(x)+d-(y),d-(x)+d+(y)}=n-2,则有向图D含有向Hamilton路;2)如果对任意具有共同内邻点或者具有共同的外邻点的非邻接顶点对{x,y},都有d(x)+d(y)≥(5/2)n-5,则有向图D含有向Hamilton路.更多还原

【Abstract】 Using some relevant theorems and results of graph theory, two sufficient conditions of digraph with directed Hamiltonian path are studied. That is, let \%D\% be a strongly connected digraph with \%n\%≥2 vertices: 1) Suppose that \%d(x)+d(y)≥2n+1\%, and min{\%d\++(x)+d\+-(y),d\+-(x)+d\++(y)}\% for every pair of nonadjacent vertices \%x,y∈V(D)\% with a common inneighbour or a common outneighbour, then \%D\% has a directed Hamiltonian path; 2) Suppose that \%d(x)+d(y)≥(5/2)n-5\%, for every pair of nonadjacent vertices \%x,y∈V(D)\% with a common inneighbour or a common outneighbour, then \%D\% has a directed Hamiltonian path. Further, the two sufficient conditions are proved.更多还原