圖中有邊不交的3個1─因子的一個新充分條件

A New Sufficient Condition for A Graph to Contain Three Disjoint 1-Factors

摘要: Win于1982年證明了2n階Ore-(1)型圖有邊不交的3個1-因子.本文改進這個結果,得到一個新的充分條件:2n(n ≥ 10)階2-連通Ore-(-2)型圖G有邊不交的1個Hamilton圖和1個1-因子,除非G是附圖中所示的圖之一.

Abstract: It was proved by S Win in 1982 that every Ore-type-(1) graph of order 2ⁿ has a Hamilton cycle and a 1-factor which are edge-disjoint.In this paper, we obtain the following theorem Every 2-connected Ore-type-(-2) graph G of order 2n(n ≥ 10) has a Hamilton cycle and a 1-factor which are edge-disjoint unless G is one of the graphs in Figure.