Abstract
AbstractWin conjectured that a graph on vertices contains disjoint perfect matchings, if the degree sum of any two nonadjacent vertices is at least , where is even and . In this paper, we prove that Win's conjecture is true for , where is sufficiently large. To show this result, we prove a theorem on ‐factor in a graph under some Ore‐type condition. Our main tools include Tutte's ‐factor theorem, the Karush‐Kuhn‐Tucker theorem on convex optimization and the solution to the long‐standing 1‐factor decomposition conjecture.
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