【摘要】 图G=（V,E）被称为点可迹的,如果对任意一点u,G中存在Hamilton链使u为其一端点;图G被称为{u}-Hamilton链连通的,如果对任意v∈V\u,G中存在Ha-milton链使u,v为其两端点。对于任意V₀V,0≤|V₀|≤h（或V₀V\u.0≤|V₀|≤h）,如果G\V₀是点可迹的（或{u}-Hamilton连通的）,则称G为h-点可迹的（或h-{u}-Hamilton连通的）。本文证明了:若G是h-点可迹的（或h-{u}-Hamilton连通的）,则其幂图G^h是（h+2k-2）-点可迹的（或（h+2k-2）-{u}-Hamilton连通的）（|V|≥h+2k+1）。更多还原

【Abstract】 A graph G = (V, E) is called vertex-traceable, if for any u∈V, there exists a Hamiltonian path in G such that u is an endpoint of the path; G is called Hamiltonian-connected from u, if for any v∈V\u, there exists a Hamiltonian path in G such that u and v are two endpoints of the path. For any F0 V, 0≤|Vo|≤h (or V0 V\u, 0≤ |V0|≤h), if G\V0 is vertex-traceable (or Hamiltonian-connected from u) , then G is called h-vertex-traceable (or h-Hamiltonian-connected from u). In this paper, we will prove: if G is h-vertex-traccable (or h-Hamiltonian-connected from u), then the kth power of G, Gk, is h-vertex-traceable {or (h + 2k- 2) -Hamiltonian-connected from u, with |V|≥h+2k+1}.更多还原