Hamilton Cycles in the Graphs of Ore-Type-(1)
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摘要: 1982年Win證明了:2n階Ore-(1)型圖G有邊不交的一個Hamilton圈和一個1-因子。本文證明了:在幾乎與Win定理的條件相同的情況下,Ore-(1)型圖有邊不交的兩個Hamilton圈和一個1-因子。Abstract: It was proved by S. Win in 1982 that if the sum of the degree of nonadjacent vertices of a simple graph G of order 2n is at least 2n + 1, then G has a Hamilton cycle and a 1-factor which are edge-disjoint. In this paper, it is proved that, under almost the same condition as Win's theorem, G has at least two Hamilton cycles and a 1-factor which are edge-disjoint.
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Key words:
- Hamilton cycle /
- 1-factor /
- Ore-type-(1)
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