We use YouTube Live to broadcast seminar talks live if the speaker agrees.

### Dabeen Lee (이다빈), On a generalization of the Chvátal-Gomory closure

Room B232 IBS (기초과학연구원)

Integer programming is the problem of optimizing a linear function over the set of integer solutions satisfying a system of inequalities. The most successful technique in practice is the so-called "cutting-plane" algorithm in combination with branch-and-bound enumeration. Cutting-planes for an integer linear program are linear inequalities that are valid for all integer feasible solutions but

### Kevin Hendrey, Covering radius in the Hamming permutation space

Room B232 IBS (기초과학연구원)

Our problem can be described in terms of a two player game, played with the set $\mathcal{S}_n$ of permutations on $\{1,2,\dots,n\}$. First, Player 1 selects a subset $S$ of $\mathcal{S}_n$ and shows it to Player 2. Next, Player 2 selects a permutation $p$ from $\mathcal{S}_n$ as different as possible from the permutations in $S$, and shows it to Player

### Ringi Kim (김린기), The strong clique number of graphs with forbidden cycles

Room B232 IBS (기초과학연구원)

The strong clique number of a graph $G$ is the maximum size of a set of edges of which every pair has distance at most two. In this talk, we prove that every  $\{C_5,C_{2k}\}$-free graph has strong clique number at most $k\Delta(G)-(k-1)$, which resolves a conjecture by  Cames van Batenburg et al. We also prove

### Pascal Gollin, Disjoint dijoins for classes of dibonds in finite and infinite digraphs

Room B232 IBS (기초과학연구원)

A dibond in a directed graph is a bond (i.e. a minimal non-empty cut) for which all of its edges are directed to a common side of the cut. A famous theorem of Lucchesi and Younger states that in every finite digraph the least size of an edge set meeting every dicut equals the maximum

### Casey Tompkins, Saturation problems in the Ramsey theory of graphs, posets and point sets

Room B232 IBS (기초과학연구원)

In 1964, Erdős, Hajnal and Moon introduced a saturation version of Turán's classical theorem in extremal graph theory. In particular, they determined the minimum number of edges in a $K_r$-free, $n$-vertex graph with the property that the addition of any further edge yields a copy of $K_r$. We consider analogues of this problem in other

### Sang-il Oum (엄상일), Survey on vertex-minors

Room B232 IBS (기초과학연구원)

For a vertex v of a graph G, the local complementation at v is an operation to obtain a new graph denoted by G*v from G such that two distinct vertices x, y are adjacent in G*v if and only if both x, y are neighbors of v and x, y are non-adjacent, or at least one

### Seunghun Lee (이승훈), Leray numbers of complexes of graphs with bounded matching number

Room B232 IBS (기초과학연구원)

Given a graph $G$ on the vertex set $V$, the non-matching complex of $G$, $\mathsf{NM}_k(G)$, is the family of subgraphs $G' \subset G$ whose matching number $\nu(G')$ is strictly less than $k$. As an attempt to generalize the result by Linusson, Shareshian and Welker on the homotopy types of $\mathsf{NM}_k(K_n)$ and $\mathsf{NM}_k(K_{r,s})$ to arbitrary graphs

### Eun Jung Kim (김은정), Twin-width: tractable FO model checking

Room B232 IBS (기초과학연구원)

Inspired by a width invariant defined on permutations by Guillemot and Marx , we introduce the notion of twin-width on graphs and on matrices. Proper minor-closed classes, bounded rank-width graphs, map graphs, $K_t$-free unit $d$-dimensional ball graphs, posets with antichains of bounded size, and proper subclasses of dimension-2 posets all have bounded twin-width. On all these classes

### O-joung Kwon (권오정), Mim-width: a width parameter beyond rank-width

Room B232 IBS (기초과학연구원)

Vatshelle (2012) introduced a width parameter called mim-width. It is based on the following cut function : for a vertex partition (A,B) of a graph, the complexity of this partition is computed by the size of a maximum induced matching of the bipartite subgraph induced by edges between A and B. This parameter naturally extends

### Hong Liu (刘鸿), Asymptotic Structure for the Clique Density Theorem

Room B232 IBS (기초과학연구원)

The famous Erdős-Rademacher problem asks for the smallest number of r-cliques in a graph with the given number of vertices and edges. Despite decades of active attempts, the asymptotic value of this extremal function for all r was determined only recently, by Reiher . Here we describe the asymptotic structure of all almost extremal graphs.

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr