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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-ORIGINAL-URL:https://dimag.ibs.re.kr
X-WR-CALDESC:Events for Discrete Mathematics Group
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BEGIN:VTIMEZONE
TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
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DTSTART:20210101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220803T163000
DTEND;TZID=Asia/Seoul:20220803T173000
DTSTAMP:20260419T041713
CREATED:20220720T073000Z
LAST-MODIFIED:20240707T075557Z
UID:5637-1659544200-1659547800@dimag.ibs.re.kr
SUMMARY:Lars Jaffke\, Taming graphs with no large creatures and skinny ladders
DESCRIPTION:We confirm a conjecture of Gartland and Lokshtanov [arXiv:2007.08761]: if for a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no member of $\mathcal{G}$ contains a $k$-creature as an induced subgraph or a $k$-skinny-ladder as an induced minor\, then there exists a polynomial $p$ such that every $G \in \mathcal{G}$ contains at most $p(|V(G)|)$ minimal separators. By a result of Fomin\, Todinca\, and Villanger [SIAM J. Comput. 2015] the latter entails the existence of polynomial-time algorithms for Maximum Weight Independent Set\, Feedback Vertex Set and many other problems\, when restricted to an input graph from $\mathcal{G}$. Furthermore\, as shown by Gartland and Lokshtanov\, our result implies a full dichotomy of hereditary graph classes defined by a finite set of forbidden induced subgraphs into tame (admitting a polynomial bound of the number of minimal separators) and feral (containing infinitely many graphs with exponential number of minimal separators). \nJoint work with Jakub Gajarský\, Paloma T. Lima\, Jana Novotná\, Marcin Pilipczuk\, Paweł Rzążewski\, and Uéverton S. Souza.
URL:https://dimag.ibs.re.kr/event/2022-08-03/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220810T163000
DTEND;TZID=Asia/Seoul:20220810T173000
DTSTAMP:20260419T041713
CREATED:20220713T073000Z
LAST-MODIFIED:20240705T171145Z
UID:5849-1660149000-1660152600@dimag.ibs.re.kr
SUMMARY:Akash Kumar\, Random walks and Forbidden Minors
DESCRIPTION:Random walks and spectral methods have had a strong influence on modern graph algorithms as evidenced by the extensive literature on the subject. In this talk\, I will present how random walks helped make progress on algorithmic problems on planar graphs.\nIn particular\, I show how random walk based (i.e.\, spectral) approaches led to progress on finding forbidden minors [K.-Seshadhri-Stolman\, FOCS 2018] as well as on deciding planarity [K.-Seshadhri-Stolman\, STOC 2019] in bounded degree graphs within the property testing framework. I will also cover how these approaches eventually led to progress on the so-called “efficient partition oracle” problem [K.-Seshadhri-Stolman\, FOCS 2021].\nThe talk will assume minimal background by presenting a stand-alone story that should be of interest to students/researchers in computer science.
URL:https://dimag.ibs.re.kr/event/2022-08-10/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220825T100000
DTEND;TZID=Asia/Seoul:20220825T110000
DTSTAMP:20260419T041713
CREATED:20220825T010000Z
LAST-MODIFIED:20240707T075527Z
UID:6007-1661421600-1661425200@dimag.ibs.re.kr
SUMMARY:Brett Leroux\, Expansion of random 0/1 polytopes
DESCRIPTION:A conjecture of Milena Mihail and Umesh Vazirani states that the edge expansion of the graph of every $0/1$ polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used to generate an element from a set of combinatorial objects uniformly at random. A weaker form of the conjecture of Mihail and Vazirani says that the edge expansion of the graph of a $0/1$ polytope in $\mathbb{R}^d$ is greater than 1 over some polynomial function of $d$. This weaker version of the conjecture would suffice for all applications. Our main result is that the edge expansion of the graph of a random $0/1$ polytope in $\mathbb{R}^d$ is at least $\frac{1}{12d}$ with high probability. \nAfter discussing this result and the proof\, we will mention some possible extensions. To conclude\, we will discuss some related questions about the combinatorics of random polytopes\, including the diameter problem. \nThis is joint work with Luis Rademacher.
URL:https://dimag.ibs.re.kr/event/2022-08-25/
LOCATION:Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]
CATEGORIES:Virtual Discrete Math Colloquium
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20220831T163000
DTEND;TZID=Asia/Seoul:20220831T173000
DTSTAMP:20260419T041713
CREATED:20220816T233139Z
LAST-MODIFIED:20240707T075512Z
UID:6033-1661963400-1661967000@dimag.ibs.re.kr
SUMMARY:Raphael Steiner\, Congruence-constrained subdivisions in digraphs
DESCRIPTION:I will present the short proof from [1] that for every digraph F and every assignment of pairs of integers $(r_e\,q_e)_{e\in A(F)}$ to its arcs\, there exists an integer $N$ such that every digraph D with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of length congruent to $r_e$ modulo $q_e$ for every $e \in  A(F)$. This generalizes to the directed setting the analogous result by Thomassen for undirected graphs and at the same time yields a novel proof of his result. I will also talk about how a hypergraph coloring result from [2] may help to obtain good bounds on $N$ in the special case when $F$ is subcubic. \n[1] https://arxiv.org/abs/2208.06358 \n[2] https://arxiv.org/abs/2206.13635
URL:https://dimag.ibs.re.kr/event/2022-08-31/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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