### 88th KPPY Combinatorics Workshop -- Aug 31, 2018

 Date: Aug 31, 2018 Time: 11:00am-5:30pm Location: Science Building 1, Room 417Department of Mathematics, Yeungnam University

 Schedule 11:00 - 11:50 Eun-Kyung Cho PNU On sharp sufficient conditions for the existence of an even $[a,b]$-factor in a graph Lunch 1:30 -2:20 Seunghwan Yang Intellicon Lab Web crawling and scraping (I) 2:30 -3:20 Seunghwan Yang Intellicon Lab. Web crawling and scraping (II) 3:40 - 4:30 Suyoung Choi Ajou University Betti number of real toric varieties associated to Weyl chambers 4:40 - 5:30 Suil O SUNY Korea Sharp Spectral Bounds for the Edge-connectivity of a Simple Regular Graph Banquet
Program

## Abstracts

Eun-Kyung Cho
On sharp sufficient conditions for the existence of an even $[a,b]$-factor in a graph
Let $a$ and $b$ be positive integers. An even $[a,b]-$factor of a graph $G$ is a spanning subgraph $H$ such that for every vertex $v \in V(G)$, $d_H(v)$ is even and $a \le d_H(v) \le b$. In 2005, Matsuda proposed a conjecture on a sufficient condition for the existence of an even $[a,b]$-factor. He proved that the conjecture is true when $a = 2$ and $n \geq b+3$. In this talk, we show that the conjecture does not hold when $a = 2$ and $n = b+2$ or $a > 2$ by presenting counterexamples and prove some sharp sufficient conditions for the existence of an even $[a,b]$-factor in a graph.

This is joint work with Jong Yoon Hyun, Suil O, and Jeong-Rye Park.
Seunghwan Yang
Web crawling and scraping (I)
In this talk, we study what about the web crawling and scraping for data. We briefly introduce how to use Python. By using Python, we practice to bring the data in a website.
Seunghwan Yang
Web crawling and scraping (II)
In this talk, we study what about the web crawling and scraping for data. We briefly introduce how to use Python. By using Python, we practice to bring the data in a website.
Suyoung Choi
Betti number of real toric varieties associated to Weyl chambers
Given a root system, the Weyl chambers in the co-weight lattice give rise to a real toric variety, called the real toric variety associated to the Weyl chambers. We compute the integral cohomology groups of real toric varieties associated to the Weyl chambers of classical types.
Suil O
Sharp Spectral Bounds for the Edge-connectivity of a Simple Regular Graph
Let $\lambda_2(G)$ be the second largest eigenvalue of a graph $G$, and let $\kappa'(G)$ be the minimum size of an edge set $S$ such that $G-S$ is disconnected. For $t=1$ or $2$, Cioaba determined the best upper bounds for $\lambda_2(G)$ in a $d$-regular simple graph $G$ to guarantee that $\kappa'(G) \ge t+1$. In this talk, we give the best upper bounds for all $t \ge 3$.

This is joint work with Jongyook Park, Jungrae Park, and Hyunju Yu.