2023 Vertex-Minor Workshop

SONO BELLE Jeju

This workshop aims to foster collaborative discussions and explore the various aspects of vertex-minors, including structural theory and their applications. This event will be small-scale, allowing for focused talks and meaningful interactions among participants. Website: https://indico.ibs.re.kr/event/596/

Matija Bucić, Essentially tight bounds for rainbow cycles in proper edge-colourings

Room B332 IBS (기초과학연구원)

An edge-coloured graph is said to be rainbow if it uses no colour more than once. Extremal problems involving rainbow objects have been a focus of much research over the last decade as they capture the essence of a number of interesting problems in a variety of areas. A particularly intensively studied question due to

Robert Hickingbotham, Powers of planar graphs, product structure, and blocking partitions

Room B332 IBS (기초과학연구원)

Graph product structure theory describes complex graphs in terms of products of simpler graphs. In this talk, I will introduce this subject and talk about some of my recent results in this area. The focus of my talk will be on a new tool in graph product structure theory called `blocking partitions.’ I’ll show how

The 3rd East Asia Workshop on Extremal and Structural Graph Theory

The Southern Beach Hotel & Resort Okinawa

The 3rd East Asia Workshop on Extremal and Structural Graph Theory is a workshop to bring active researchers in the field of extremal and structural graph theory, especially in the East Asia such as China, Japan, and Korea. Website: http://tgt.ynu.ac.jp/2023EastAsia.html

Bruce A. Reed, Some Variants of the Erdős-Sós Conjecture

Room B332 IBS (기초과학연구원)

Determining the density required to ensure that a host graph G contains some target graph as a subgraph or minor is a natural and well-studied question in extremal combinatorics. The celebrated 50-year-old Erdős-Sós conjecture states that for every k, if G has average degree exceeding k-2 then it contains every tree T with k vertices

Seunghun Lee (이승훈), On colorings of hypergraphs embeddable in $\mathbb{R}^d$

Room B332 IBS (기초과학연구원)

Given a hypergraph $H=(V,E)$, we say that $H$ is (weakly) $m$-colorable if there is a coloring $c:V\to $ such that every hyperedge of $H$ is not monochromatic. The (weak) chromatic number of $H$, denoted by $\chi(H)$, is the smallest $m$ such that $H$ is $m$-colorable. A vertex subset $T \subseteq V$ is called a transversal

Hyunwoo Lee (이현우), Towards a high-dimensional Dirac’s theorem

Room B332 IBS (기초과학연구원)

Dirac's theorem determines the sharp minimum degree threshold for graphs to contain perfect matchings and Hamiltonian cycles. There have been various attempts to generalize this theorem to hypergraphs with larger uniformity by considering hypergraph matchings and Hamiltonian cycles. We consider another natural generalization of the perfect matchings, Steiner triple systems. As a Steiner triple system

Ben Lund, Almost spanning distance trees in subsets of finite vector spaces

Room B332 IBS (기초과학연구원)

For $d\ge 2$ and an odd prime power $q$, let $\mathbb{F}_q^d$ be the $d$-dimensional vector space over the finite field $\mathbb{F}_q$. The distance between two points $(x_1,\ldots,x_d)$ and $(y_1,\ldots,y_d)$ is defined to be $\sum_{i=1}^d (x_i-y_i)^2$. An influential result of Iosevich and Rudnev is: if $E \subset \mathbb{F}_q^d$ is sufficiently large and $t \in \mathbb{F}_q$, then

Ting-Wei Chao (趙庭偉), Tight Bound on Joints Problem and Partial Shadow Problem

Room B332 IBS (기초과학연구원)

Given a set of lines in $\mathbb R^d$, a joint is a point contained in d linearly independent lines. Guth and Katz showed that N lines can determine at most $O(N^{3/2})$ joints in $\mathbb R^3$ via the polynomial method. Yu and I proved a tight bound on this problem, which also solves a conjecture proposed

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IBS Discrete Mathematics Group (DIMAG)
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