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

Date: | Aug 31, 2018 | |

Time: | 11:00am-5:30pm | |

Location: | Science Building 1, Room 417 Department 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 |

## Abstracts

Eun-Kyung Cho

On sharp sufficient conditions for the existence of an even $[a,b]$-factor in a graph

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.

This is joint work with Jong Yoon Hyun, Suil O, and Jeong-Rye Park.

Seunghwan Yang

Web crawling and scraping (I)

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)

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

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

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.

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