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DTSTART:20230101T000000
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DTSTART;TZID=Asia/Seoul:20241203T163000
DTEND;TZID=Asia/Seoul:20241203T173000
DTSTAMP:20260417T043224
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UID:10022-1733243400-1733247000@dimag.ibs.re.kr
SUMMARY:Yulai Ma\, Pairwise disjoint perfect matchings in regular graphs
DESCRIPTION:An $r$-graph is an $r$-regular graph in which every odd set of vertices is connected to its complement by at least $r$ edges. A central question regarding $r$-graphs is determining the maximum number of pairwise disjoint perfect matchings they can contain. This talk explores how edge connectivity influences this parameter. \nFor ${0 \leq \lambda \leq r}$\, let $m(\lambda\,r)$ denote the maximum number $s$ such that every $\lambda$-edge-connected $r$-graph contains $s$ pairwise disjoint perfect matchings. The values of $m(\lambda\,r)$ are known only in limited cases; for example\, $m(3\,3)=m(4\,r)=1$\, and $m(r\,r) \leq r-2$ for all $r \not = 5$\, with $m(r\,r) \leq r-3$ when $r$ is a multiple of $4$. In this talk\, we present new upper bounds for $m(\lambda\,r)$ and examine connections between $m(5\,5)$ and several well-known conjectures for cubic graphs. \nThis is joint work with Davide Mattiolo\, Eckhard Steffen\, and Isaak H. Wolf.
URL:https://dimag.ibs.re.kr/event/2024-12-03/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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