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DTSTART:20240101T000000
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DTSTART;TZID=Asia/Seoul:20250401T163000
DTEND;TZID=Asia/Seoul:20250401T173000
DTSTAMP:20260417T014154
CREATED:20250310T023035Z
LAST-MODIFIED:20250310T023155Z
UID:10673-1743525000-1743528600@dimag.ibs.re.kr
SUMMARY:Hyunwoo Lee (이현우)\, Reconstructing hypergraph matching polynomials
DESCRIPTION:By utilizing the recently developed hypergraph analogue of Godsil’s identity by the second author\, we prove that for all $n \geq k \geq 2$\, one can reconstruct the matching polynomial of an $n$-vertex $k$-uniform hypergraph from the multiset of all induced sub-hypergraphs on $\lfloor \frac{k-1}{k}n \rfloor + 1$ vertices. This generalizes the well-known result of Godsil on graphs in 1981 to every uniform hypergraph. As a corollary\, we show that for every graph $F$\, one can reconstruct the number of $F$-factors in a graph under analogous conditions. We also constructed examples that imply the number $\lfloor \frac{k-1}{k}n \rfloor + 1$ is the best possible for all $n\geq k \geq 2$ with $n$ divisible by $k$. This is joint work Donggyu Kim.
URL:https://dimag.ibs.re.kr/event/2025-04-01/
LOCATION:Room B332\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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