### Alan Lew, Representability and boxicity of simplicial complexes

Zoom ID: 934 3222 0374 (ibsdimag)

An interval graph is the intersection graph of a family of intervals in the real line. Motivated by problems in ecology, Roberts defined the boxicity of a graph G to be the minimal k such that G can be written as the intersection of k interval graphs. A natural higher-dimensional generalization of interval graphs is

### Hongseok Yang (양홍석), DAG-symmetries and Symmetry-Preserving Neural Networks

Room B232 IBS (기초과학연구원)

The preservation of symmetry is one of the key tools for designing data-efficient neural networks. A representative example is convolutional neural networks (CNNs); they preserve translation symmetries, and this symmetry preservation is often attributed to their success in real-world applications. In the machine-learning community, there is a growing body of work that explores a new

### Jeong Ok Choi (최정옥), Invertibility of circulant matrices of arbitrary size

Room B232 IBS (기초과학연구원)

In this talk, we present sufficient conditions to guarantee the invertibility of rational circulant matrices with any given size. These sufficient conditions consist of linear combinations in terms of the entries in the first row with integer coefficients. Using these conditions we show the invertibility of some family of circulant matrices with particular forms of

### Florian Gut and Attila Joó, Large vertex-flames in uncountable digraphs

Zoom ID: 934 3222 0374 (ibsdimag)

The local connectivity  $\kappa_D(r,v)$ from $r$ to $v$ is defined to be the maximal number of internally disjoint $r\rightarrow v$ paths in $D$. A spanning subdigraph $L$ of $D$ with $\kappa_L(r,v)=\kappa_D(r,v)$ for every $v\in V-r$ must have at

### Suil O (오수일), Eigenvalues and [a, b]-factors in regular graphs

Room B232 IBS (기초과학연구원)

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

### Jaehoon Kim (김재훈), $K_{r+1}$-saturated graphs with small spectral radius

Room B232 IBS (기초과학연구원)

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

### Stefan Weltge, Integer programs with bounded subdeterminants and two nonzeros per row

Room B232 IBS (기초과학연구원)

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

### Semin Yoo (유세민), Combinatorics of Euclidean spaces over finite fields

Room B232 IBS (기초과학연구원)

$q$-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

### Euiwoong Lee (이의웅), The Karger-Stein algorithm is optimal for k-cut

Room B232 IBS (기초과학연구원)

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

### Maria Chudnovsky, Induced subgraphs and tree decompositions

Zoom ID: 934 3222 0374 (ibsdimag)

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. Tree decompositions are closely related to the existence of "laminar collections of separations" in a graph, which roughly means that

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IBS Discrete Mathematics Group (DIMAG)
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