Color-bias perfect matchings in hypergraphs

Abstract

We study conditions under which an edge-colored hypergraph has a particular substructure that contains more than the trivially guaranteed number of monochromatic edges. Our main result solves this problem for perfect matchings under minimum degree conditions. This answers recent questions of Gishboliner, Glock, and Sgueglia and of Balogh, Treglown, and Zárate-Guerén.

Hiˆe.p Hàn was supported by the ANID Regular grant 1231599 and by ANID Basal Grant CMM FB210005, Richard Lang was supported by the EU Horizon 2020 programme MSCA (101018431), Jo˜ao Pedro Marciano was partially supported by FAPERJ (Proc. E-26/200.977/2021) and CAPES, Matías Pavez-Signé was supported by ANID-FONDECYT Regular grant 1241398 and ANID Basal Grant CMM FB210005, Nicolás Sanhueza-Matamala was supported by ANID-FONDECYT Iniciación Nº11220269 grant and ANID-FONDECYT Regular Nº1251121 grant, Andrew Treglown was supported by EPSRC grant EP/V048287/1, and Camila ZárateGuerén was supported by EPSRC. Open access statement. This research was funded in part by EPSRC grant EP/V048287/1. For the purpose of open access, a CC BY public copyright licence is applied to any Author Accepted Manuscript arising from this submission.

Peer Reviewed

Postprint (author's final draft)