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DTSTART;TZID=Asia/Seoul:20211026T163000
DTEND;TZID=Asia/Seoul:20211026T173000
DTSTAMP:20260424T080623
CREATED:20211026T073000Z
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UID:4709-1635265800-1635269400@dimag.ibs.re.kr
SUMMARY:Donggyu Kim (김동규)\, 𝝘-graphic delta-matroids and their applications
DESCRIPTION:Bouchet (1987) defined delta-matroids by relaxing the base exchange axiom of matroids. Oum (2009) introduced a graphic delta-matroid from a pair of a graph and its vertex subset. We define a $\Gamma$-graphic delta-matroid for an abelian group $\Gamma$\, which generalizes a graphic delta-matroid. \nFor an abelian group $\Gamma$\, a $\Gamma$-labelled graph is a graph whose vertices are labelled by elements of $\Gamma$. We prove that a certain collection of edge sets of a $\Gamma$-labelled graph forms a delta-matroid\, which we call a $\Gamma$-graphic delta-matroid\, and provide a polynomial-time algorithm to solve the separation problem\, which allows us to apply the symmetric greedy algorithm of Bouchet (1987) to find a maximum weight feasible set in such a delta-matroid. We also prove that a $\Gamma$-graphic delta-matroid is a graphic delta-matroid if and only if it is even. We prove that every $\mathbb{Z}_p^k$-graphic delta matroid is represented by some symmetric matrix over a field of characteristic of order $p^k$\, and if every $\Gamma$-graphic delta-matroid is representable over a finite field $\mathbb{F}$\, then $\Gamma$ is isomorphic to $\mathbb{Z}_p^k$ and $\mathbb{F}$ is a field of order $p^\ell$ for some prime $p$ and positive integers $k$ and $\ell$. \nThis is joint work with Duksang Lee and Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-10-26/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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