Pure Mathematics Colloquium - New results on properties of algebraic constructions of extremal graph theory

Dates

Tuesday, December 6, 2022 - 14:00 to 15:00

Speaker:  Vasyl Ustimenko (Royal Holloway, University of London)

Abstract: For an arbitrary finite field Fq, q>2 we prove that known q-regular algebraic bipartite graphs A(n,q) on 2qn vertices have girth 2n or 2n+2. A similar result is formulated for more general graphs A(n,K) defined over a general commutative integrity ring K. The impact of these results on Extremal Graph Theory and its applications will be discussed.

This research is partially supported by the Fellowship of British Academy for Researchers at Risk 2022.