### 80th KPPY Combinatorics Workshop -- Dec 17, 2016

 Date: Dec 17, 2016 Time: 11:00am-6:00pm Location: Science Building No. 1, Room 319, Department of Mathematics in Yeungnam University

 Schedule 11:00 - 11:50 Shingo Saito Kyushu University Bowman-Bradley type theorems for multiple zeta values and analogues 12:00 Lunch 1:40 - 2:30 Min Jae Kwon Kyungpook National University The Krull dimension of composite power series rings over valuation rings 2:40 - 3:30 Seog-Jin Kim Konkuk University List 3-dynamic coloring of graphs with small maximum average degree 4:00 - 4:50 Kyoung-tark Kim Sogang University Power series Ore's extension 5:00 - 5:50 O-joung Kwon Technische Universitat Berlin Coloring graphs without fan vertex-minors 6:30 - 8:30 Banquet
Program

## Abstracts

Shingo Saito
Bowman-Bradley type theorems for multiple zeta values and analogues
Multiple zeta values are a multivariate analogue of special values of the Riemann zeta function. After giving a brief introduction to the theory of multiple zeta values, I shall present results related to a formula established by Bowman and Bradley.
Min Jae Kwon
The Krull dimension of composite power series rings over valuation rings
The problem of determining the Krull dimension of the polynomial ring $R[X]$ and the power series ring $R[[X]]$ is one of the problems in commutative rings. When $\dim(R)$ is finite, $\dim(R[X])$ was completely determined. In power series case, there are some difficulties. For example, $R[[X]]$ may have uncountable Krull dimension even if $\dim(R) = 1$. In traditional power series extension, many results were showed. But in composite power series extension, only some results were discovered. In this talk, I will introduce some tools to construct prime chains and classify the Krull dimension of composite power series rings over valuation rings.
Seog-Jin Kim
List 3-dynamic coloring of graphs with small maximum average degree
An $r$-dynamic $k$-coloring of a graph $G$ is a proper $k$-coloring $\phi$ such that for any vertex $v$, $v$ has at least $\min\{r,\deg_G(v) \}$ distinct colors in $N_G(v)$. The $r$-dynamic chromatic number $\chi_r^d(G)$ of a graph $G$ is the least $k$ such that there exists an $r$-dynamic $k$-coloring of $G$. The list $r$-dynamic chromatic number of a graph $G$ is denoted by $ch_r^d(G)$. Recently, Loeb, Mahoney, Reiniger, and Wise showed that the list $3$-dynamic chromatic number of a planar graph is at most 10. And Cheng, Lai, Lorenzen, Luo, Thompson, and Zhang studied the maximum average degree condition to have $\chi_3^d (G) \leq 4, \ 5$, or $6$. In this paper, we study list 3-dynamic coloring in terms of maximum average degree. We show that $ch^d_3(G) \leq 6$ if $mad(G) < \frac{18}{7}$, and $ch^d_3(G) \leq 7$ if $mad(G) < \frac{14}{5}$, and both of the bounds are tight. This is joint work with Boram Park.
Kyoung-tark Kim
Power series Ore's extension
Recently, there was a chance to look at again the definitions of p-adic integers, p-adic numbers, and Witt vectors. I thought (conjecturally) that these constructions can be unified in terms of (a generalization of) Ore's extension. I will provide also some history of embedding problem of a domain into its quotient skew field: When is a ring without zero divisors embedded in a division ring? This subject is my current research in progress.
O-joung Kwon
Coloring graphs without fan vertex-minors
A graph class $C$ is called chi-bounded if there is a function $f$ such that for every graph $G$ in $C$, the chromatic number of $G$ is bounded by $f(w(G))$ where $w(G)$ is the size of a maximum clique in $G$. Geelen conjectured that for every graph $H$, the class of $H$ vertex-minor free graphs is chi-bounded. We prove that this conjecture is true when $H$ is a fan graph. This is joint work with Choi and Oum.