BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Hongliang Lu (XJTU) DTSTART:20200903T070000Z DTEND:20200903T080000Z DTSTAMP:20260423T021017Z UID:SCMSComb/14 DESCRIPTION:Title: Co-degree condition for matchings in $k$-partite $k$-graphs\nby Hon gliang Lu (XJTU) as part of SCMS Combinatorics Seminar\n\n\nAbstract\nLet $H$ be a $k$-partite $k$-graph with $n$ vertices in each partition class\ , and let\n$\\delta_{k-1}(H)$ denote the minimum co-degree of $H$. We cha racterize those $H$ with $\\delta_{k-1}(H) \\geq n/2$ and with no perfect matching. As a consequence we give an affirmative answer to the following question of R\\"odl and Ruci\\'nski: If $k$ is even or $n \\not\\equiv 2 \ \pmod 4$\, does $\\delta_{k-1}(H) \\geq n/2$ imply that $H$ has a perfect matching? We give an example indicating that it is not sufficient to impo se this degree bound on only two types of $(k-1)$-sets. For near perfect m atching\, we gave a tight sufficient condition in term of co-degree\, whic h is also independently obtained by Han\, Zang and Zhao. Moreover\, I woul d like to introduce several problems I am interested in.\n\npassword 12132 3\n LOCATION:https://researchseminars.org/talk/SCMSComb/14/ END:VEVENT END:VCALENDAR