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

Thursday (Sep 26, 2024), 4:00-5:00 pm: Ngo Viet Trung (Institute of Mathematics, Vietnam Academy of Science and Technology)
Ear decompositions of graphs$\colon$ an unexpected tool in Combinatorial Commutative Algebra
Abstract(Click to expand) Ear decomposition is a classical notion in Graph Theory. It has been shown in [1, 2] that this notion can be used to solve difficult problems on homological properties of edge ideals in Combinatorial Commutative Algebra. This talk presents the main combinatorial ideas behind these results.
 
[1] H.M. Lam and N.V. Trung, Associated primes of powers of edge ideals and ear decompositions of graphs, Trans. AMS 372 (2019)
[2] H.M. Lam, N.V. Trung, and T.N. Trung, A general formula for the index of depth stability of edge ideals, Trans. AMS, to appear.
Place: 5101, the 5th Teaching Building
Thursday (Dec 21, 2023), 3:00-4:00 pm: Xiaofan Yuan (Arizona State University)
Rainbow Connectivity in Edge-colored Graphs
Abstract(Click to expand) Fujita and Magnant proved that if the minimum color degree of an edge-colored graph $(G,c)$ of order $n (>2)$ is at least $n/2$, then each pair of vertices in $(G,c)$ is connected by a properly-colored path. We show that for large $n$, the same minimum color degree condition implies rainbow connectivity of the edge-colored graph; that is, each pair of vertices in $(G,c)$ is connected by a path whose edges are distinctly colored. This is joint work with Andrzej Czygrinow.
Place: 5206, the 5th Teaching Building

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