A BK inequality for random matchings

A BK inequality for random matchings

Let $G=(S,T,E)$ be a bipartite graph. For a matching $M$ of $G$ , let $V(M)$ be the set of vertices covered by $M$ , and let $B(M)$ be the symmetric difference of $V(M)$ and $S$ . We prove that if $M$ is a uniform random matching of $G$ , then $B(M)$ satisfies the BK inequality for increasing events...

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Veröffentlicht in:Combinatorics, probability & computing probability & computing, 2023-01, Vol.32 (1), p.151-157
1. Verfasser: Mészáros, András
Format: Artikel
Sprache:eng
Schlagworte:
Apexes
Decomposition
Graph theory
Graphs
Inequality
Matching
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Beschreibung
Zusammenfassung:Let $G=(S,T,E)$ be a bipartite graph. For a matching $M$ of $G$ , let $V(M)$ be the set of vertices covered by $M$ , and let $B(M)$ be the symmetric difference of $V(M)$ and $S$ . We prove that if $M$ is a uniform random matching of $G$ , then $B(M)$ satisfies the BK inequality for increasing events.
ISSN:0963-5483
1469-2163
DOI:10.1017/S0963548322000189