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During the 2021 Spring semester, the Discrete Mathematics/Algebra Seminar will meet on Wednesdays between 1:20pm and 2:20pm US Eastern time.
If you wish to receive the Zoom link, please email the organizer, Sebastian Cioaba.
| Sayan Mukherjee, University of Illinois at Chicago | Sayan Mukherjee, University of Illinois at Chicago | Zoom | <br>
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Title: An extension of D(k,q) to triple systems
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Abstract: Constructing bipartite graphs of high edge density and high girth is one of the major open problems in extremal graph theory. We consider an extension of this problem to triple systems. Using an extension of the bipartite graphs D(k,q) introduced by Lazebnik, Ustimenko and Woldar, we prove that the largest number of triples in a triple system on n vertices not containing the 6-cycle in any link graph is of the order of magnitude n^(7/3). We also explore the prospects of extending the proof to larger even cycles. | 4/21/2021 5:20:00 PM | 4/21/2021 6:20:00 PM | False | |
| Mark Kempton, Brigham Young University | Mark Kempton, Brigham Young University | Zoom | <br>
Title: Spectral Properties of Non-backtracking Random Walks
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Abstract: Random walks on graphs play a critical role in modern graph theory and in many graph algorithms. Spectral properties of matrices associated with a graph are key in understanding random walks. A natural modification of a random walk is to forbid backtracking -- that is, the random walk cannot return to the vertex visited on the previous step. In this talk, I will discuss matrices that can be associated to a graph that describe non-backtracking walks, and will look at spectral properties of those matrices. | 4/28/2021 5:20:00 PM | 4/28/2021 6:20:00 PM | False | |
| Ruth Luo, University of California, San Diego | Ruth Luo, University of California, San Diego | Zoom | <br>
Title: Super-pancyclic graphs
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Abstract: We say a hypergraph H is super-pancyclic if for every set of vertices A, there exists a Berge cycle of H whose base vertices are exactly the vertices in A. In this talk, we give necessary conditions for a hypergraph to be super-pancyclic and also prove that these conditions are sufficient in certain classes of hypergraphs. We will also discuss related problems for finding Berge cycles in hypergraphs. This is joint work with Misha Lavrov, Alexandr Kostochka, and Dara Zirlin.
| 5/5/2021 5:20:00 PM | 5/5/2021 6:20:00 PM | False | |
| Nathan Lindzey, University of Colorado, Boulder | Nathan Lindzey, University of Colorado, Boulder | Zoom | Title: TBA
Abstract: TBA | 5/12/2021 5:20:00 PM | 5/12/2021 6:20:00 PM | False | |
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