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Perfect matchings in hyperfinite graphings

De Marcin Sabok

Apparaît dans la collection : XVI International Luminy Workshop in Set Theory / XVI Atelier international de théorie des ensembles

We characterize hyperfinite bipartite graphings that admit measurable perfect matchings. In particular, we prove that every regular hyperfinite one-ended bipartite graphing admits a measurable perfect matching. We give several applications of this result. We extend the Lyons-Nazarov theorem by showing that a bipartite Cayley graph admits a factor of iid perfect matching if and only if the group is not iso-morphic to the semidirect product of Z and a finite group of odd order, answering a question of Kechris and Marks in the bipartite case. We also answer an open question of Bencs, Hruskova and Toth arising in the study of balanced orientations in graphings. Finally, we show how our results generalize and lead to a simple approach to recent results on measurable circle squaring.

Informations sur la vidéo

Date de captation 16/09/2021
Date de publication 04/10/2021
Institut CIRM
Licence CC BY NC ND
Langue Anglais
Audience Chercheurs
Réalisateur(s) Guillaume Hennenfent
Format MP4

Données de citation

DOI 10.24350/CIRM.V.19809703
Citer cette vidéo Sabok, Marcin (16/09/2021). Perfect matchings in hyperfinite graphings. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19809703
URL https://dx.doi.org/10.24350/CIRM.V.19809703

Domaine(s)

Bibliographie

Bowen, Matthew, Gabor Kun, and Marcin Sabok. "Perfect matchings in hyperfinite graphings." arXiv preprint arXiv:2106.01988 (2021). - https://arxiv.org/abs/2106.01988

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