增广立方体中经过给定三条边的哈密尔顿圈

Hamilton Cycle Passing Through Prescribed Edges in Augmented Cube

用归纳假设法证明了结论:令AQn是增广立方体,当n≥2时,若EeE(AQn),1≤︱Ee︱≤3,这里Ee是线性森林(每个分支都是路),则在AQn中有哈密尔顿圈包含Ee的所有边.

In this paper, the following result is obtained. LetAQnbe the augmented cube, wheren≥2,E, E（AQn）, with 1≤ ｜Ee｜≤3, the subgraph induced by E, is a linear forest （i.e..pairwise vertex-disjoint paths ）,then all edges of Ee lie on a Hamilton cycle in the graph AQn.