Graph Theory Seminar: Zero-Sum Ramsey Number of Bounded Degree Graphs

Abstract:

Given a graph H, the classical Ramsey problem asks for the smallest integer n such that any red-blue colouring of the edges of a clique on n vertices contains a monochromatic copy of H. In 1990 Bialostocki and Dierker introduced an algebraic variant of this problem called zero-sum Ramsey theory, in which we instead colour the edges of the clique with elements of a finite abelian group and look for a copy of H such that the sum of the colours on its edges is 0.

We show that for any finite abelian group G and any graph H with bounded maximum degree, the zero-sum Ramsey number of H in G is linear in the number of edges of H. In this talk, we introduce the background of zero-sum Ramsey theory and give an outline of the proof used for this result. We highlight the difficulties when looking at general finite abelian groups, as opposed to cyclic groups, and explain how these can be overcome.

This is joint work with Xiaopan Lian, Alexandru Malekshahian and Andrey Shapiro.

Speaker: Jasmin Katz (LSE)
When: Wednesday, May 13, 2026, 10:00 AM
Venue: John von Neumann Room, 7th Floor, CMM