Kaohsiung, Taiwan

**Venue:** College of Science Room SC4009-1, National Sun Yat-sen University

**Venue:** [ trasportation campus map ]

**Poster:** [ pdf ]

**Announcements:**

- [20240129] Photos uploaded.
- [20231118] Registration is open.
- [20231116] Schedule is available.
- [20231105] Welcome to SZWM2024!

The conference's primary objective is to create a conducive environment where researchers can exchange findings, insights, and challenges within the fields of graph theory, combinatorics, and their practical applications. It encompasses a comprehensive range of topics in discrete mathematics and their real-world implementations, with a particular focus on the intersection with artificial intelligence. This conference represents a continuation of previous gatherings at NSYSU, paying tribute to the individuals who have made substantial contributions to our shared endeavors.

Each talk is **40 minutes for presentation** and **10 minuntes for questions**.

- 09:30Registration & Coffee Break
- 09:50Opening Remark
- 10:00
**Xuding Zhu**, Zhejiang Normal UniversityTruncated-degree-choosability of graphs## Abstract

Assume $G$ is a graph and $k$ is a positive integer. Let $f: V(G) \to \mathbb{N}$ be defined as $f(v)=\min\{k, d_G(v)\}$. If $G$ is $f$-choosable (respectively, DP-$f$-colourable), then we say $G$ is $k$-truncated-degree-choosable (respectively, DP-$k$-truncated-degree-colourable). Richter asked whether every 3-connected non-complete planar graph is 6-truncated-degree-choosable. Motivated by Richter's question, Hutchinson proved that $2$-connected maximal outerplanar graphs other than the triangle are $5$-truncated-degree-choosable in 2008. Recently, Dai, Hu, Li, and Maezawa proved that $2$-connected outerplanar graphs other than cycles are DP-$5$-truncated-degree-colourable. Richter's question remained open. We answer Ricter's question in negative by constructing a $3$-connected non-complete planar graph which is not $7$-truncated-degree-choosable. On the other hand, we prove that every $3$-connected non-complete planar graph is $12$-truncated-degree-choosable. We also prove that 2-connected $K_{2,4}$-minor free graphs are DP-$5$-truncated-degree-colourable. These results are proved in three papers that are joint work with Huan Zhou and Jialu Zhu, On-Hei Solomon Lo, Cheng Wang and Huan Zhou, Huijuan Xu and Xinbo Xu, respectively.

- 11:00
**Michael Fuchs**, National Chengchi UniversityGalled tree-child networks## Abstract

Phylogenetics is concerned with understanding classical and reticulate evolution where phylogenetic trees are used as model for the former and phylogenetic networks as model for the latter. Enumerating and studying properties of a "typical" network, i.e., a network picked uniformly at random from one of the many network classes is a new and emerging field in phylogenetics. (On the other hand, enumeration results and random properties of phylogenetic trees are largely known.) For example, such results have been proved for the classes of tree-child networks and galled networks with very different (combinatorial) tools. So, how about tree-child networks which also have the galled property, i.e., galled tree-child networks? In this talk, we will present our recent results for this class which contain (asymptotic) enumeration results and limit laws for the number of reticulation vertices of a random galled tree-child networks. The talk is based on (upcoming) joint work with Yu-Sheng Chang (National Chengchi University) and Guan-Ru Yu (National Sun Yat-sen University).

- 12:00Lunch Time
- 14:00
**Sen-Peng Eu**, National Taiwan Normal UniversityFrom boustrophedon to Euler numbers and beyond## Abstract

Starting with an algorithm inspired by an ancient writing system (boustrophedon) an integer array can be generated. Surprisingly, the sums of the rows of the array turn out to be Euler numbers, which are ubiquitous in many branches of mathematics. From this we survey and relate the boustrophedon to our recent work on its Coxeter combinatorial generalizations, namely the Springer numbers and Arnold families.

- 15:00
**Wei-Liang Sun**, National Taiwan Normal UniversityCyclotomic numbers, Schur rings and their applications## Abstract

Cyclotomic numbers represent the cardinalities of intersections of specific subsets within a finite field. These numbers emerged in discussions related to C. F. Gauss's exploration of the constructibility of regular polygons and were subsequently investigated by L. E. Dickson in the study of Waring's problem. Building upon these pioneering works, extensive studies on cyclotomic numbers have flourished. These include applications in combinatorial design, cryptography, and information theory. A subtle connection exists between cyclotomic numbers and Schur rings, a particular type of subrings within group rings. I. Schur introduced these rings as he extended W. Burnside's studies on permutation groups (using terminology different from modern conventions). Schur rings were also found to have applications in solving the graph isomorphism problem in the 1970s. In this talk, we will discuss these topics, their applications and some conjectures.

- 16:00Group Photo & Coffee Break
- 16:20
**Jephian C.-H. Lin**, National Sun Yat-sen UniversitySpectral Clustering: Theory and Practice## Abstract

Given a graph and a function on its vertices, how do we partition the vertices into clusters so that (1) vertices with similar function values are in the same cluster and (2) the induced subgraph on each cluster is connected as much as possible? Such a problem has applications in detecting the sources of air pollution, image segmentation, and so on. We will go through the theoretical background of this algorithm and demonstrate some of its applications.

- 17:20Free Discussions
- 17:36Sunset @ Sizihwan Bay

There is no default arrangement for dinner. You are welcome to stay, and we may have an **informal gathering at our own cost**.

- Jephian C.-H. Lin, National Sun Yat-sen University
- Yuan-Hsun Lo, National Pingtung University
- Tsai-Lien Wong, National Sun Yat-sen University
- Guan-Ru Yu, National Sun Yat-sen University
- Xuding Zhu, Zhejiang Normal University

- National Sun Yat-sen University