The Erdős–Ko–Rado theorem for 2-intersecting families of perfect matchings
Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 575-598.

A perfect matching in the complete graph on 2k vertices is a set of edges such that no two edges have a vertex in common and every vertex is covered exactly once. Two perfect matchings are said to be t-intersecting if they have at least t edges in common. The main result in this paper is an extension of the famous Erdős–Ko–Rado (EKR) theorem [4] to 2-intersecting families of perfect matchings for all values of k. Specifically, for k3 a set of 2-intersecting perfect matchings in K 2k of maximum size has (2k-5)(2k-7)(1) perfect matchings.

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DOI: https://doi.org/10.5802/alco.169
Classification: 05E30,  05C50,  05C25
Keywords: Erdős–Ko–Rado Theorem, Perfect matchings, Association scheme, Ratio bound, Clique, Coclique, Quotient graphs, Character table.
@article{ALCO_2021__4_4_575_0,
     author = {Fallat, Shaun and Meagher, Karen and Shirazi, Mahsa N.},
     title = {The {Erd\H{o}s{\textendash}Ko{\textendash}Rado} theorem for 2-intersecting families of perfect matchings},
     journal = {Algebraic Combinatorics},
     pages = {575--598},
     publisher = {MathOA foundation},
     volume = {4},
     number = {4},
     year = {2021},
     doi = {10.5802/alco.169},
     language = {en},
     url = {https://alco.centre-mersenne.org/articles/10.5802/alco.169/}
}
Fallat, Shaun; Meagher, Karen; Shirazi, Mahsa N. The Erdős–Ko–Rado theorem for 2-intersecting families of perfect matchings. Algebraic Combinatorics, Volume 4 (2021) no. 4, pp. 575-598. doi : 10.5802/alco.169. https://alco.centre-mersenne.org/articles/10.5802/alco.169/

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