# Welcome to the USTC Combinatorics Group

This is the homepage of the Combinatorics Group at the School of Mathematical Sciences, University of Science and Technology of China (USTC).

Our research interests cover various branches of Combinatorics, including graph theory, extremal combinatorics, probabilistic combinatorics, combinatorial design, and their applications to theoretical computer science, information theory and optimization.

We are looking for highly motivated Postdocs, PhD students, and Master students to join the group (more info) !

#### Talks

Friday (Dec 16, 2022), 10:30-11:20 pm: Weifan Wang (Zhejiang Normal University)
Arboricity and Partition video
Abstract(Click to expand) For a positive integer $n$, the linear $n$-arboricity of a graph $G$ is the least number $k$ such that $G$ can be edge-partitioned into $k$ forests, whose component trees are paths of length at most $n$. When $n$ is infinite, the corresponding parameter is called the linear arboricity of $G$. In this talk, we give a survey for the research progress about the arboricity, linear arboricity, linear $2$-arboricity and other edge-partition problems of graphs. Some unsolved problems will be provided.
Tencent Meeting: 840231948
Passcode: 1958

Thursday (Dec 15, 2022), 2-3 pm: Changhong Lu (East China Normal University)
A bridge between the coin-weighing problem and the double resolving problem of graphs video
Abstract(Click to expand) 硬币称重问题（Coin-weighing problems）是个经典的组合优化问题，其中一个经典形式为：给定$n$个硬币，假定真硬币的重量和假硬币的重量均已知，用弹簧称对硬币进行称重，用最少的称重次数将所有的假币找出来。图的$2$-分辨集（double resolving problem）是Caceres 等人在2007年为了研究图的分辨集问题（resolving set problem）提出的一个工具性的新概念。最近，我们证明了超方体的$2$-分辨集问题与硬币称重问题的等价关系，我们利用硬币称重问题的Lindström方法给出计算超方体和折叠超方体$2$-分辨集问题的快速算法，给出了一些新结果，包括解决公开问题；反过来，$2$-分辨集问题的图论结果也给硬币称重问题带来了一些新进展，比如$14$,$16$,$18$个硬币称重问题的新上界。
Tencent Meeting: 578277138
Passcode: 1958