超立方图和超立方有向图的同构因子分解

Isomorphic factorization of hypercube graphs and hypercube digraphs

图Ｇ＝（Ｖ，Ｅ）的一个同构因子分解是边集Ｅ的一个划分：｛Ｅ１，Ｅ２，…，Ｅｔ｝，使得生成子图（Ｖ， Ｅ１），…，（Ｖ，Ｅｔ）都彼此同构。若 Ｈ≌（Ｖ，Ｅ１），记为 Ｈ［Ｇ或 ｔ］Ｇ．若对每个ｔ≥２．当 时．均有：ｔＧ，则称Ｇ为有理图．文章证明了超立方图（ｈｙｐｅｒｃｕｂｅ）和超立方有向图都是有理图．

An isomorphic factorization of a graph G = (V, E) is a partition {E1, E2, ... Et} of E such that (V, E,) (V, E2) ... (V, E,). We then write H|G or t|G, if such a factorization exists. G is said to be rational if t|G always exists for all t>2 and t||E (G)|. It is proved that hypercube graphs and hypercube digraphs are rational.