Affiliation:
1. Institut für Informatik Universität Heidelberg Heidelberg Deutschland
Abstract
AbstractWe prove that in all regular robust expanders , every edge is asymptotically equally likely contained in a uniformly chosen perfect matching . We also show that given any fixed matching or spanning regular graph in , the random variable is approximately Poisson distributed. This in particular confirms a conjecture and a question due to Spiro and Surya, and complements results due to Kahn and Kim who proved that in a regular graph every vertex is asymptotically equally likely contained in a uniformly chosen matching. Our proofs rely on the switching method and the fact that simple random walks mix rapidly in robust expanders.
Funder
Deutsche Forschungsgemeinschaft
Subject
Applied Mathematics,Computer Graphics and Computer-Aided Design,General Mathematics,Software
Reference10 articles.
1. Perfect Matchings in $\epsilon$-regular Graphs
2. A.Ferber K.Hänni andV.Jain.The probability of selectingk$$ k $$edge‐disjoint Hamilton cycles in the complete graph. arXiv:2001.01149.2020.
3. Cycle partitions of regular graphs
4. D.Johnston P. M.Kayll andC.Palmer.Deranged matchings: proofs and conjectures. arXiv:2209.11319.2022.
5. Fractional cycle decompositions in hypergraphs
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