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PRODID:-//Discrete Mathematics Group - ECPv6.15.20//NONSGML v1.0//EN
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X-WR-CALNAME:Discrete Mathematics Group
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
BEGIN:STANDARD
TZOFFSETFROM:+0900
TZOFFSETTO:+0900
TZNAME:KST
DTSTART:20200101T000000
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210706T163000
DTEND;TZID=Asia/Seoul:20210706T173000
DTSTAMP:20260423T052550
CREATED:20210518T100610Z
LAST-MODIFIED:20240707T081252Z
UID:4101-1625589000-1625592600@dimag.ibs.re.kr
SUMMARY:Suil O (오수일)\, Eigenvalues and [a\, b]-factors in regular graphs
DESCRIPTION:For positive integers\, $r \ge 3\, h \ge 1\,$ and $k \ge 1$\, Bollobás\, Saito\, and Wormald proved some sufficient conditions for an $h$-edge-connected $r$-regular graph to have a k-factor in 1985. Lu gave an upper bound for the third-largest eigenvalue in a connected $r$-regular graph to have a $k$-factor in 2010. Gu found an upper bound for certain eigenvalues in an $h$-edge-connected $r$-regular graph to have a $k$-factor in 2014. For positive integers $a \le b$\, an even (or odd) $[a\, b]$-factor of a graph $G$ is a spanning subgraph $H$ such that for each vertex $v \in V (G)$\, $d_H(v)$ is even (or odd) and $a \le d_H(v) \le b$. In this talk\, we provide best upper bounds (in terms of $a\, b$\, and $r$) for certain eigenvalues (in terms of $a\, b\, r$\, and $h$) in an $h$-edge-connected $r$-regular graph $G$ to guarantee the existence of an even $[a\, b]$-factor or an odd $[a\, b]$-factor. This result extends the one of Bollobás\, Saito\, and Wormald\, the one of Lu\, and the one of Gu.
URL:https://dimag.ibs.re.kr/event/2021-07-06/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210713T163000
DTEND;TZID=Asia/Seoul:20210713T173000
DTSTAMP:20260423T052550
CREATED:20210519T133727Z
LAST-MODIFIED:20240707T081244Z
UID:4110-1626193800-1626197400@dimag.ibs.re.kr
SUMMARY:Jaehoon Kim (김재훈)\, $K_{r+1}$-saturated graphs with small spectral radius
DESCRIPTION:For a graph $H$\, a graph $G$ is $H$-saturated if $G$ does not contain $H$ as a subgraph but for any $e\in E(\overline G)$\, $G+e$ contains $H$. In this note\, we prove a sharp lower bound for the number of paths and walks on length 2 in $n$-vertex $K_{r+1}$-saturated graphs. We then use this bound to give a lower bound on the spectral radii of such graphs which is asymptotically tight for each fixed $r$ and $n\to \infty$.
URL:https://dimag.ibs.re.kr/event/2021-07-13/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210714T170000
DTEND;TZID=Asia/Seoul:20210714T180000
DTSTAMP:20260423T052550
CREATED:20210615T091821Z
LAST-MODIFIED:20240705T184018Z
UID:4257-1626282000-1626285600@dimag.ibs.re.kr
SUMMARY:Stefan Weltge\, Integer programs with bounded subdeterminants and two nonzeros per row
DESCRIPTION:We give a strongly polynomial-time algorithm for integer linear programs defined by integer coefficient matrices whose subdeterminants are bounded by a constant and that contain at most two nonzero entries in each row. The core of our approach is the first polynomial-time algorithm for the weighted stable set problem on graphs that do not contain more than k vertex-disjoint odd cycles\, where k is any constant. Previously\, polynomial-time algorithms were only known for k=0 (bipartite graphs) and for k=1. \nWe observe that integer linear programs defined by coefficient matrices with bounded subdeterminants and two nonzeros per column can be also solved in strongly polynomial-time\, using a reduction to b-matching. \nThis is joint work with Samuel Fiorini\, Gwenaël Joret\, and Yelena Yuditsky.
URL:https://dimag.ibs.re.kr/event/2021-07-14/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Virtual Discrete Math Colloquium
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210720T163000
DTEND;TZID=Asia/Seoul:20210720T173000
DTSTAMP:20260423T052550
CREATED:20210601T234138Z
LAST-MODIFIED:20240707T081226Z
UID:4190-1626798600-1626802200@dimag.ibs.re.kr
SUMMARY:Semin Yoo (유세민)\, Combinatorics of Euclidean spaces over finite fields
DESCRIPTION:$q$-analogues of quantities in mathematics involve perturbations of classical quantities using the parameter $q$\, and revert to the original quantities when $q$ goes $1$. An important example is the $q$-analogues of binomial coefficients\, denoted by $\binom{n}{k}_{q}$\, which give the number of $k$-dimensional subspaces in $\mathbb{F}_{q}^{n}$. When $q$ goes to $1$\, this reverts to the binomial coefficients which measure the number of $k$-sets in $\left [ n \right ]$. \nIn this talk\, we add one more structure in $\mathbb{F}_{q}^{n}$\, which is the Euclidean quadratic form: $\text{dot}_{n}:=x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}$. It turns out that the number of quadratic subspaces of Euclidean type in $(\mathbb{F}_{q}^{n}\,\text{dot}_{n})$ can be described as the form of the analogue of binomial coefficients. The main goal of this talk is to define the dot-analogues of the binomial coefficients and to study related combinatorics. No prior knowledge about the theory of quadratic form is required.
URL:https://dimag.ibs.re.kr/event/2021-07-20/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210727T150000
DTEND;TZID=Asia/Seoul:20210727T160000
DTSTAMP:20260423T052550
CREATED:20210623T055635Z
LAST-MODIFIED:20240707T081214Z
UID:4288-1627398000-1627401600@dimag.ibs.re.kr
SUMMARY:Euiwoong Lee (이의웅)\, The Karger-Stein algorithm is optimal for k-cut
DESCRIPTION:In the k-cut problem\, we are given an edge-weighted graph and want to find the least-weight set of edges whose deletion breaks the graph into k connected components. It is easy to see that the elegant randomized contraction algorithm of Karger and Stein for global mincut (k=2) can be naturally extended for general k with the running time of $O(n^{2k-2})$. Using tree packings\, Thorup gave a deterministic algorithm that has the same running time. \nIn this work\, we show that for any fixed $k\ge 2$\, the Karger-Stein algorithm outputs any fixed minimum k-cut with probability at least $\Omega(n^{-k})$. This also gives an extremal bound of $O(n^k)$ on the number of minimum k-cuts in an n-vertex graph and an algorithm to compute a minimum k-cut in similar runtime. Both are essentially tight. The first main ingredient in our result is a fine-grained analysis of how the graph shrinks—and how the average degree evolves—under the Karger-Stein process. The second ingredient is an extremal result bounding the number of cuts of size at most $(2-\delta)OPT/k$\, using the Sunflower lemma. \nJoint work with Anupam Gupta\, David G. Harris\, and Jason Li.
URL:https://dimag.ibs.re.kr/event/2021-07-27/
LOCATION:Room B232\, IBS (기초과학연구원)
CATEGORIES:Discrete Math Seminar
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BEGIN:VEVENT
DTSTART;TZID=Asia/Seoul:20210728T150000
DTEND;TZID=Asia/Seoul:20210728T160000
DTSTAMP:20260423T052550
CREATED:20210607T135955Z
LAST-MODIFIED:20240705T184022Z
UID:4228-1627484400-1627488000@dimag.ibs.re.kr
SUMMARY:Maria Chudnovsky\, Induced subgraphs and tree decompositions
DESCRIPTION:Tree decompositions are a powerful tool in structural graph theory; they are traditionally used in the context of forbidden graph minors. Connecting tree decompositions and forbidden induced subgraphs has until recently remained out of reach. \nTree decompositions are closely related to the existence of  “laminar collections of separations” in a graph\, which roughly means that the separations in the collection “cooperate” with each other\, and the pieces that are obtained when the graph is simultaneously decomposed by all the separations in the collection “line up” to form a tree structure. Such collections of separations come up naturally in the context of forbidden minors. \nIn the case of families where induced subgraphs are excluded\, while there are often natural separations\, they are  usually very far from forming a laminar collection. In what follows we mostly focus on families of graphs of bounded degree. It turns out that due to the bound on the degree\, these collections of natural separations can be partitioned into a bounded number of laminar collections. This in turn allows to us obtain a wide variety of structural and algorithmic results\, which we will survey in this talk.
URL:https://dimag.ibs.re.kr/event/2021-07-28/
LOCATION:Zoom ID: 869 4632 6610 (ibsdimag)
CATEGORIES:Virtual Discrete Math Colloquium
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