Stability for 1-intersecting families of perfect matchings
نویسندگان
چکیده
منابع مشابه
An algebraic proof of the Erdős-Ko-Rado theorem for intersecting families of perfect matchings
In this paper we give a proof that the largest set of perfect matchings, in which any two contain a common edge, is the set of all perfect matchings that contain a fixed edge. This is a version of the famous Erdős-Ko-Rado theorem for perfect matchings. The proof given in this paper is algebraic, we first determine the least eigenvalue of the perfect matching derangement graph and use properties...
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A conjecture of G. Fan and A. Raspaud asserts that every bridgeless cubic graph contains three perfect matchings with empty intersection. We suggest a possible approach to problems of this type, based on the concept of a balanced join in an embedded graph. We use this method to prove a special case of a conjecture of E. Máčajová and M. Škoviera on Fano colorings of cubic graphs.
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We consider the following generalization of the seminal Erdős–Ko–Rado theorem, due to Frankl [5]. For some k ≥ 2, let F be a k-wise intersecting family of r-subsets of an n element set X, i.e. for any F1, . . . , Fk ∈ F , ∩ k i=1Fi 6= ∅. If r ≤ (k − 1)n k , then |F| ≤ ( n−1 r−1 ) . We prove a stability version of this theorem, analogous to similar results of Dinur-Friedgut, Keevash-Mubayi and o...
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We find recursive formulae for the number of perfect matchings in a graph G by splitting G into subgraphs H and Q. We use these formulas to count perfect matching of P hypercube Qn. We also apply our formulas to prove that the number of perfect matching in an edge-transitive graph is , where denotes the number of perfect matchings in G, is the graph constructed from by deleting edges with an en...
متن کاملStability for Intersecting Families in PGL(2, q)
We consider the action of the 2-dimensional projective general linear group PGL(2, q) on the projective line PG(1, q). A subset S of PGL(2, q) is said to be an intersecting family if for every g1, g2 ∈ S, there exists α ∈ PG(1, q) such that αg1 = αg2 . It was proved by Meagher and Spiga that the intersecting families of maximum size in PGL(2, q) are precisely the cosets of point stabilizers. We...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2020
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2020.103091