Algebra and Combinatorics Seminar

Date: September 16, 2022

Time: 3:00PM - 4:00PM

Location: BLOC 302

Speaker: Youngho Yoo, TAMU

Title: A unified Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups

Abstract: Erdős and Pósa showed in 1965 that cycles obey an approximate packing-covering duality. While odd cycles do not satisfy such a duality, Reed proved that the only obstruction is the presence of a certain projective planar grid. In this talk we discuss generalizations of these results. Namely, in undirected group-labelled graphs, we characterize the topological obstructions to the Erdős-Pósa property of cycles with "allowable" group values, under some additional assumptions on the structure of the set of allowable values. This recovers many known results in the area and resolves a question of Dejter and Neumann-Lara from 1987 on characterizing when cycles of length L mod M satisfy the Erdős-Pósa property. Joint work with Pascal Gollin, Kevin Hendrey, O-joung Kwon, and Sang-il Oum.