Two Results on Win's Conjecture

Gen Zhibin. Two Results on Win's Conjecture[J]. Geomatics and Information Science of Wuhan University, 1992, 17(1): 83-88.

Citation:

Gen Zhibin. Two Results on Win's Conjecture[J]. Geomatics and Information Science of Wuhan University, 1992, 17(1): 83-88.

Citation:

Gen Zhibin. Two Results on Win's Conjecture[J]. Geomatics and Information Science of Wuhan University, 1992, 17(1): 83-88.

Abstract

Let G be a simple graph on 2n vertices and k an integer satisfying -1≤k, If d(u)+d(v)≥2n+k for every two nonadjacent verfices u and v of the graph G, then G is said to be the graph of Ore-type-(k). S. Win¹ gave the folloing conjecture:If G is the graph Ore-type-(k), then G contains k+2 disjoint 1-factors, where k≤2n-4.In this paper, we proved that Win's conjecture is tre for k=2n-4, 2u-5.

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