Seminar

I am one of the members organizing Incheon Combinatorics Seminar. We organize meetings in Thursday (Incheon National University, Inha University) or Friday (SUNY Korea) for this spring semester. We are happy to invite you to give a talk. Please e-mail me if you are interested in.

 

DATE : 11th, Oct, 2018 (10am-3pm)
There will be a one-day graph theory workshop at INU. Detailed information can be found at http://ojkwon.com/seminar/inugraph/.

DATE : 5th, Apr, 2018 (4-5pm).
TITLE: Sharp bound on the number of maximal sum-free subsets of integers
SPEAKER : Hong Liu

ABSTRACT : Cameron and Erd\H{o}s asked whether  the number of \emph{maximal} sum-free sets in $\{1, \dots , n\}$ is much smaller than the  number of sum-free sets. In the same paper they gave a lower bound of $2^{\lfloor n/4 \rfloor }$ for the number of maximal sum-free sets. We resolved this problem, proving that for each $1\leq i \leq 4$, there is a constant $C_i$ such that, given any $n\equiv i \mod 4$, $\{1, \dots , n\}$ contains  $(C_i+o(1)) 2^{n/4}$ maximal sum-free sets.
Our proof makes use of  container and removal lemmas of Green,  a structural result of Deshouillers, Freiman, S\’os and Temkin and a recent bound on the number of subsets of integers with small sumset by Green and Morris. We also discuss related results and open problems on the number of maximal sum-free subsets of abelian groups. Joint work with Jozsef Balogh, Maryam Sharifzadeh and Andrew Treglown.

DATE : 19th, Apr, 2018 (4:20-5:10pm).
TITLE: Forbidding induced even cycles in a graph: typical structure and counting
SPEAKER : Jaehoon Kim

ABSTRACT : We determine, for all k6, the typical structure of graphs that do not contain an induced 2k-cycle. This verifies a conjecture of Balogh and Butterfield. Surprisingly, the typical structure of such graphs is richer than that encountered in related results. The approach we take also yields an approximate result on the typical structure of graphs without an induced 8-cycle or without an induced 10-cycle.

DATE : 12th, June, 2018 (4:00-4:50pm).
TITLE: Helly type theorems in combinatorics
SPEAKER : Minki Kim

ABSTRACT : Helly’s theorem is one of the most well-known and fundamental result about intersection patterns of convex in Euclidean spaces. It asserts that for a finite family $\mathcal{F}$ of convex sets in $\mathbb{R}^d$, if every $d+1$ or fewer members of $\mathcal{F}$ have a point in common, then all members of the family $\mathcal{F}$ have a point in common. There are a remarkable number of variants and applications of Helly’s theorem, and these results are called Helly type theorems. In this talk, I will give a brief overview on classical Helly type theorems, and introduce some recent generalizations of Helly’s theorem.