## 2019 IBS Summer Research Program on Algorithms and Complexity in Discrete Structures

July 21st, 2019

2019 IBS Summer Research Program on Algorithms and Complexity in Discrete Structures

## July 21 Sunday – August 10 Saturday

Room B232, IBS (기초과학연구원)

## Schedule

### July 22 Monday

10:00-11:00 Introduction

11:00-12:00 Open Problems

### July 23 Tuesday

11:00-10:30 Stefan Kratsch, Humboldt-Universität zu Berlin, Germany
Elimination Distances, Blocking Sets, and Kernels for Vertex Cover

10:45-11:15 Benjamin Bergougnoux, University Clermont Auvergne, France
More applications of the d-neighbor equivalence

11:30-12:00 Yixin Cao, Hong Kong Polytechnic University, China
Enumerating Maximal Induced Subgraphs

### July 24 Wednesday

(We will go to KAIST for June Huh‘s two talks 15:00-16:00, 16:30-17:30.)

### July 25 Thursday

10:00-11:00 Nick Brettell, Eindhoven University of Technology, Netherlands
Recent work on characterising matroids representable over finite fields

11:30-12:00 Mamadou M. Kanté, University Clermont Auvergne, France
On recognising k-letter graphs

### July 26 Friday

10:00-11:00 O-joung Kwon (권오정), Incheon National University, Korea
The grid theorem for vertex-minors

11:00-12:00 Progress Report

### July 27 Saturday

8:30 Excursion to Damyang (departure from the accommodation)

### July 29 Monday

10:00-11:00 Archontia Giannopoulou, National and Kapodistrian University of Athens, Greece
The directed flat wall theorem

11:30-12:00 Eunjung Kim (김은정), LAMSADE-CNRS, France
Subcubic even-hole-free graphs have a constant treewidth

### July 30 Tuesday

10:00-11:00 Pierre Aboulker, ENS Ulm, France
Generalizations of the geometric de Bruijn Erdős Theorem

11:30-12:00 Michael Dobbins, Binghamton University, USA
Barycenters of points in polytope skeleta

### July 31 Wednesday

10:00-11:00 Magnus Wahlström, Royal Holloway, University of London, UK
T.B.A.

11:30-12:00 Édouard Bonnet, ENS Lyon, France
The FPT/W[1]-hard dichotomy of Max Independent Set in H-free graphs

### August 1 Thursday

10:00-11:00 Euiwoong Lee (이의웅), NYU, USA
Losing treewidth by separating subsets

11:30-12:00 Sang-il Oum (엄상일), IBS Discrete Mathematics Group and KAIST, Korea
Branch-depth: Generalizing tree-depth of graphs

### August 2 Friday

10:00-11:00 Dabeen Lee (이다빈), IBS Discrete Mathematics Group, Korea
t-perfect graphs and the stable set problem

11:00-12:00 Progress Report

August 5-9: Free Discussions / Research Collaborations / Progress Report
Tea time: Every weekday 3:30pm

## Mihyun Kang (강미현), The genus of a random graph and the fragile genus property

June 28th, 2019

IBS/KAIST Joint Discrete Math Seminar

The genus of a random graph and the fragile genus property
2019/08/20 Tue 4:30PM-5:30PM
In this talk we shall discuss how quickly the genus of the Erdős-Rényi random graph grows as the number of edges increases and how dramatically a small number of random edges can increase the genus of a randomly perturbed graph. (Joint work with Chris Dowden and Michael Krivelevich)

## Dabeen Lee, Integrality of set covering polyhedra and clutter minors

June 28th, 2019

IBS/KAIST Joint Discrete Math Seminar

Integrality of set covering polyhedra and clutter minors
Dabeen Lee (이다빈)
IBS Discrete Mathematics Group
2019/07/16 Tue 4:30PM-5:30PM
Given a finite set of elements $V$ and a family $\mathcal{C}$ of subsets of $V$, the set covering problem is to find a minimum cardinality subset of $V$ intersecting every subset in the family $\mathcal{C}$. The set covering problem, also known as the hitting set problem, admits a simple integer linear programming formulation. The constraint system of the integer linear programming formulation defines a polyhedron, and we call it the set covering polyhedron of $\mathcal{C}$. We say that a set covering polyhedron is integral if every extreme point is an integer lattice point. Although the set covering problem is NP-hard in general, conditions under which the problem becomes polynomially solvable have been studied. If the set covering polyhedron is integral, then it is straightforward that the problem can be solved using a polynomial-time algorithm for linear programming.

In this talk, we will focus on the question of when the set covering polyhedron is integral. We say that the family $\mathcal{C}$ is a clutter if every subset in $\mathcal{C}$ is inclusion-wise minimal. As taking out non-minimal subsets preserves integrality, we may assume that $\mathcal{C}$ is a clutter. We call $\mathcal{C}$ ideal if the set covering polyhedron of it is integral. To understand when a clutter is ideal, the notion of clutter minors is important in that $\mathcal{C}$ is ideal if and only if so is every minor of it. We will study two fundamental classes of non-ideal clutters, namely, deltas and the blockers of extended odd holes. We will characterize when a clutter contains either a delta or the blocker of an extended odd hole as a minor.

This talk is based on joint works with Ahmad Abdi and G\’erard Cornu\’ejols.

## Patrice Ossona de Mendez, A model theoretical approach to sparsity

May 20th, 2019

IBS/KAIST Joint Discrete Math Seminar

A model theoretical approach to sparsity
2019/06/25 Tue 4:30PM-5:30PM
We discuss how the model theoretic notion of first-order transduction allows to define a notion of structural sparsity, and give some example of applications, like existence of low shrub-depth decompositions for tranductions of bounded expansion classes, characterization of transductions of classes with bounded pathwidth, decompositions of graphs with bounded rank-width into cographs.

## Suil O (오수일), An odd [1,b]-factor in regular graphs from eigenvalues

April 19th, 2019

IBS/KAIST Joint Discrete Math Seminar

An odd [1,b]-factor in regular graphs from eigenvalues
Suil O (오수일)
Department of Applied Mathematics and Statistics, SUNY-Korea
2019/06/19 Wed 4:30PM-5:30PM
An odd [1,b]-factor of a graph is a spanning subgraph H such that for every vertex v∈V(G), 1≤dH(v)≤b, and dH(v) is odd. For positive integers r≥3 and b≤r, Lu, Wu, and Yang gave an upper bound for the third largest eigenvalue in an r-regular graph with even number of vertices to guarantee the existence of an odd [1,b]-factor. In this talk, we improve their bound.