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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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TZID:Asia/Seoul
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TZOFFSETFROM:+0900
TZOFFSETTO:+0900
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DTSTART:20200101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210810T163000
DTEND;TZID=Asia/Seoul:20210810T173000
DTSTAMP:20260424T094730
CREATED:20210817T073000Z
LAST-MODIFIED:20240705T183002Z
UID:4408-1628613000-1628616600@dimag.ibs.re.kr
SUMMARY:Duksang Lee (이덕상)\, Intertwining connectivities for vertex-minors and pivot-minors
DESCRIPTION:We show that for pairs (Q\,R) and (S\,T) of disjoint subsets of vertices of a graph G\, if G is sufficiently large\, then there exists a vertex v in V(G)−(Q∪R∪S∪T) such that there are two ways to reduce G by a vertex-minor operation while preserving the connectivity between Q and R and the connectivity between S and T. Our theorem implies an analogous theorem of Chen and Whittle (2014) for matroids restricted to binary matroids. Joint work with Sang-il Oum.
URL:https://dimag.ibs.re.kr/event/2021-08-10/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210817T163000
DTEND;TZID=Asia/Seoul:20210817T173000
DTSTAMP:20260424T094730
CREATED:20210817T073000Z
LAST-MODIFIED:20240707T081153Z
UID:4242-1629217800-1629221400@dimag.ibs.re.kr
SUMMARY:Linda Cook\, Two results on graphs with holes of restricted lengths
DESCRIPTION:We call an induced cycle of length at least four a hole. The parity of a hole is the parity of its length. Forbidding holes of certain types in a graph has deep structural implications. In 2006\, Chudnovksy\, Seymour\, Robertson\, and Thomas famously proved that a graph is perfect if and only if it does not contain an odd hole or a complement of an odd hole. In 2002\, Conforti\, Cornuéjols\, Kapoor\, and Vuškovíc provided a structural description of the class of even-hole-free graphs. I will describe the structure of all graphs that contain only holes of length $\ell$ for every $\ell \geq 7$ (joint work with Jake Horsfield\, Myriam Preissmann\, Paul Seymour\, Ni Luh Dewi Sintiari\, Cléophée Robin\, Nicolas Trotignon\, and Kristina Vuškovíc. \nAnalysis of how holes interact with graph structure has yielded detection algorithms for holes of various lengths and parities. In 1991\, Bienstock showed it is NP-Hard to test whether a graph G has an even (or odd) hole containing a specified vertex $v \in V(G)$. In 2002\, Conforti\, Cornuéjols\, Kapoor\, and Vuškovíc gave a polynomial-time algorithm to recognize even-hole-free graphs using their structure theorem. In 2003\, Chudnovsky\, Kawarabayashi\, and Seymour provided a simpler and slightly faster algorithm to test whether a graph contains an even hole. In 2019\, Chudnovsky\, Scott\, Seymour\, and Spirkl provided a polynomial-time algorithm to test whether a graph contains an odd hole. Later that year\, Chudnovsky\, Scott\, and Seymour strengthened this result by providing a polynomial-time algorithm to test whether a graph contains an odd hole of length at least $\ell$ for any fixed integer $\ell \geq 5$. I will present a polynomial-time algorithm (joint work with Paul Seymour) to test whether a graph contains an even hole of length at least $\ell$ for any fixed integer $\ell \geq 4$.
URL:https://dimag.ibs.re.kr/event/2021-08-17/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210818T170000
DTEND;TZID=Asia/Seoul:20210818T180000
DTSTAMP:20260424T094730
CREATED:20210818T080000Z
LAST-MODIFIED:20240705T182104Z
UID:4353-1629306000-1629309600@dimag.ibs.re.kr
SUMMARY:Petr Hliněný\, Twin-width is linear in the poset width
DESCRIPTION:Twin-width is a new parameter informally measuring how diverse are the neighbourhoods of the graph vertices\, and it extends also to other binary relational structures\, e.g. to digraphs and posets. It was introduced quite recently\, in 2020 by Bonnet\, Kim\, Thomassé\, and Watrigant. One of the core results of these authors is that FO model checking on graph classes of bounded twin-width is in FPT. With that result\, they also claimed that posets of bounded width have bounded twin-width\, thus capturing a prior result on FO model checking of posets of bounded width in FPT. However\, their translation from poset width to twin-width was indirect and giving only a very loose double-exponential bound. \nWe prove that posets of width d have twin-width at most 9d with a direct and elementary argument\, and show that this bound is tight up to a constant factor. Specifically\, for posets of width 2\, we prove that in the worst case their twin-width is also equal to 2. These two theoretical results are complemented with straightforward algorithms to construct the respective contraction sequence for a given poset. \n(Joint work with my student Jakub Balaban who obtained the main ideas in his bachelor thesis.)
URL:https://dimag.ibs.re.kr/event/2021-08-18/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210824T163000
DTEND;TZID=Asia/Seoul:20210824T173000
DTSTAMP:20260424T094730
CREATED:20210810T073000Z
LAST-MODIFIED:20240707T081032Z
UID:4212-1629822600-1629826200@dimag.ibs.re.kr
SUMMARY:Eun Jung Kim (김은정)\, A Constant-factor Approximation for Weighted Bond Cover
DESCRIPTION:The Weighted $\mathcal F$-Vertex Deletion for a class $\mathcal F$ of graphs asks\, given a weighted graph $G$\, for a minimum weight vertex set $S$ such that $G-S\in\mathcal F$. The case when $\mathcal F$ is minor-closed and excludes some graph as a minor has received particular attention but a constant-factor approximation remained elusive for Weighted $\mathcal F$-Vertex Deletion. Only three cases of minor-closed $\mathcal F$ are known to admit constant-factor approximations\, namely Vertex Cover\, Feedback Vertex Set and Diamond Hitting Set. \nWe study the problem for the class $\mathcal F$ of $\theta_c$-minor-free graphs\, under the equivalent setting of the Weighted c-Bond Cover\, and present a constant-factor approximation algorithm using the primal-dual method. For this\, we leverage a structure theorem implicit in [Joret et al.\, SIDMA’14] which states the following: any graph $G$ containing a $\theta_c$-minor-model either contains a large two-terminal protrusion\, or contains a constant-size $\theta_c$-minor-model\, or a collection of pairwise disjoint constant-sized connected sets that can be contracted simultaneously to yield a dense graph. In the first case\, we tame the graph by replacing the protrusion with a special-purpose weighted gadget. For the second and third case\, we provide a weighting scheme which guarantees a local approximation ratio. Besides making an important step in the quest of (dis)proving a constant-factor approximation for Weighted $\mathcal F$-Vertex Deletion\, our result may be useful as a template for algorithms for other minor-closed families. \nThis is joint work with Euiwoong Lee and Dimitrios M. Thilikos.
URL:https://dimag.ibs.re.kr/event/2021-08-24/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210831T163000
DTEND;TZID=Asia/Seoul:20210831T173000
DTSTAMP:20260424T094730
CREATED:20210831T073000Z
LAST-MODIFIED:20240707T081024Z
UID:4341-1630427400-1630431000@dimag.ibs.re.kr
SUMMARY:Cheolwon Heo (허철원)\, Representations of even-cycle matroids
DESCRIPTION:A signed graph is a pair $(G\,\Sigma)$ where $G$ is a graph and $\Sigma$ is a subset of edges of $G$. A cycle $C$ of $G$ is a subset of edges of $G$ such that every vertex of the subgraph of $G$ induced by $C$ has an even degree. We say that $C$ is even in $(G\,\Sigma)$ if $|C \cap \Sigma|$ is even; otherwise\, $C$ is odd. A matroid $M$ is an even-cycle matroid if there exists a signed graph $(G\,\Sigma)$ such that circuits of $M$ precisely corresponds to inclusion-wise minimal non-empty even cycles of $(G\,\Sigma)$. For even-cycle matroids\, two fundamental questions arise:\n(1) what is the relationship between two signed graphs representing the same even-cycle matroids?\n(2) how many signed graphs can an even-cycle matroid have?\nFor (a)\, we characterize two signed graphs $(G_1\,\Sigma_1)$ and $(G_2\,\Sigma_2)$ where $G_1$ and $G_2$ are $4$-connected that represent the same even-cycle matroids.\nFor (b)\, we introduce pinch-graphic matroids\, which can generate exponentially many representations even when the matroid is $3$-connected. An even-cycle matroid is a pinch-graphic matroid if there exists a signed graph with a pair of vertices such that every odd cycle intersects with at least one of them. We prove that there exists a constant $c$ such that if a matroid is even-cycle matroid that is not pinch-graphic\, then the number of representations is bounded by $c$. This is joint work with Bertrand Guenin and Irene Pivotto.
URL:https://dimag.ibs.re.kr/event/2021-08-31/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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