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Algorithms, Combinatorics and Optimization Seminar
Joseph Briggs
Carnegie Mellon University
Title: Inverting the Turán Problem

Abstract: Classical questions in graph theory ask about ex(G,F), the maximum number of edges in an F-free subgraph of G, for some fixed family F of graphs. For example, the Turán and Zarankiewicz problems ask about ex(Kn,F) and ex(Kn,n,F) respectively. Specifically, these study the corresponding asymptotics when $n \rightarrow \infty$. Or, when F = C is the family of cycles, this becomes the graphic matroid rank, and is considered as a function of G for various different G. The second example inspires the inverted problem of optimising some monotone graph parameter over all host graphs G for which ex(G,F) = k, where now both k and F are fixed. We will explore the most natural question: what is the largest possible number of edges among all G with ex(G,F) = k? This is joint work with Christopher Cox.

Date: Thursday, September 7, 2017
Time: 3:30 pm
Location: Wean Hall 8220
Submitted by:  Bukh
Note: Before the talk, at 3:10 pm, there will be tea and cookies in Wean Hall 6220.