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

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. [ABSTRACT FROM AUTHOR]