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Algebraic approaches to EKR properties of strongly regular graphs

Sergey Goryainov

Hebei Normal University (河北师范大学)

Time: 16:00-17:00 (GMT+8), Tuesday January 9th, 2024
Location: Zoom

Abstract: In 2015, Chris Godsil and Karen Meagher proposed [GM15] systematical studies of EKR properties of strongly regular graphs. In particular, they emphasized two infinite families of strongly regular graphs: block graphs pf orthogonal arrays and block graphs of 2-designs, and posed several interesting open problems. Recently, together with my colleagues Chi Hoi Yip and Elena Konstantinova, we made a progress (in [GY23] and [GK23], respectively) towards some of the problems. In my talk, we will discuss the background on the EKR properties of strongly regular graphs and our recent results.

[GM15] C. D. Godsil, K. Meagher, Erdős-Ko-Rado Theorems: Algebraic Approaches, Cambridge University Press (2015).

[GK23] S. Goryainov, E. V. Konstantinova, Non-canonical maximum cliques without a design structure in the block graphs of 2-designs, November 2023. arXiv:2311.01190

[GY23] S. Goryainov, C. H. Yip, Extremal Peisert-type graphs without the strict-EKR property, June 2023. arXiv:2306.00391

Host: 丁兆宸 Zhaochen Ding