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Win conjectured that a graph   G   on   n   vertices contains   k   disjoint perfect matchings, if the degree sum of any two nonadjacent vertices is at least   n  +  k  −  2  , where   n   is even and   n  ≥  k  +  2  . In this paper, we prove that Win's conjecture is true for   k  ≥  n  ∕  2  , where   n   is sufficiently large. To show this result, we prove a theorem on   k  ‐factor in a graph under some Ore‐type condition. Our main tools include Tutte's   k  ‐factor theorem, the Karush‐Kuhn‐Tucker theorem on convex optimization and the solution to the long‐standing 1‐factor decomposition conjecture.

An Ore‐type condition for large k ‐factor and disjoint perfect matchings