### Eun-Kyung Cho (조은경), Decomposition of a planar graph into a $d$-degenerate graph and a graph with maximum degree at most $h$

Room B232 IBS (기초과학연구원)

Given a graph $G$, a decomposition of $G$ is a collection of spanning subgraphs $H_1, \ldots, H_t$ of $G$ such that each edge of $G$ is an edge of $H_i$ for exactly one $i \in \{1, \ldots, t\}$. Given a positive integer $d$, a graph is said to be $d$-degenerate if every subgraph of it has

### 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

Canceled

### KSIAM 2020 Spring Conference (cancelled)

IBS Science Culture Center

KSIAM 2020 Spring Conference will be held at IBS from May 8, 2020 to May 9, 2020. Organized by Korean Society for Industrial and Applied Mathematics. Organizing Committee Myungjoo Kang (Seoul National University) (chair) Ahn, Jaemyung (KAIST) Kwon, Hee-Dae (Inha University) Lee, Eun Jung (Yonsei University) Jang, Bongsoo (UNIST) Jung, Miyoun (Hankuk University of Foreign

### 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 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, Fax: +82-42-878-9209