The seminars in Discrete Mathematics are aimed at are aimed at researchers, employees, and students.
This week's seminar is given by Rik Sarkar from IISER Pune.
Title: The Mubayi-Terry Multigraph Problem
Abstract: A multigraph is called (s, q) if any set of s vertices spans at most q edges. The classical Turán problem in extremal graph theory involves finding the maximum sum of edge multiplicities in such an (s, q) multigraph. In 2016, Mubayi and Terry introduced a product version of this problem, wherein one seeks to maximize the product of edge multiplicities in an (s, q) multigraph. We prove the optimality of a broad class of Turán-type lower bound constructions for this problem, extending results by Day, Falgas-Ravry and Treglown and by Mubayi and Terry, thus resolving the problem for new infinite families of pairs (s, q). This is part of joint work with Victor Falgas-Ravry.
