The regular seminar time is Wednesday, 3:35 - 4:25 p.m. The seminar takes place in person in Stevenson Center 1308. The seminar coordinator this semester is Xiaonan Liu, xiaonan.liu at vanderbilt.edu. Some seminars may be at unusual times, or may be given as Zoom talks.
Counting k-cycles in 5-connected planar triangulations – Zhiyu Wang (Louisiana State University)
We show that every n-vertex 5-connected planar triangulation has at most 9n - 50 cycles of length 5 for all n ≥ 20, and this upper bound is tight. We also show that for every k ≥ 6, there exists some constant C(k) such that for sufficiently large n, every n-vertex 5-connected planar graph has at most C(k) · n⌊k/3⌋ cycles of length k. This upper bound is asymptotically tight for all k ≥ 6.
This is joint work with Gyaneshwar Agrahari and Xiaonan Liu.
Matroids and matroid representations – Tong Jin (Vanderbilt University)
Matroids are combinatorial abstracts of independence, a notion that appears in graph theory, linear algebra, and field extensions. In this talk, we will discuss some less-known results in matroid theory due to Tutte, which have nice consequences in matroid representation theory and excluded minor problems. This is an introductory talk; no previous knowledge on matroid theory is assumed.
Title TBA – Anna Yu (Vanderbilt University)
Title TBA – Darrion Thornburgh (Vanderbilt University)
Mark Ellingham / mark.ellingham at vanderbilt.edu