【摘要】 无向图G=(V,E)的一条边e∈E被称为是路-H am ilton边,如果存在G中的一条H am ilton-路包含e.本文描述了一类具有给定路-H am ilton边数的极图,并证明了对任意给定的一个自然数a,恰好具有a+1个顶点和a条路-H am ilton边的无向图的最大边数为[(a2+3)/4].更多还原

【Abstract】 Let G=(V,E) be an astatic graph;an edge e∈E is called path-Hamilton edge if there exists a Hamilton-path in G that contains e.After a description about category-I maximal graphs with given number of path-Hamilton edges,the authors have proved that,for any natural number a,the maximum natural number of edges for the astatic graph with exactly a+1 vertexes and a path-Hamilton edges is [(a~2+ 3)/4].更多还原