Algebra and Combinatorics Seminar

Date: February 11, 2022

Time: 3:00PM - 4:00PM

Location: Zoom

Speaker: Ryan Martin, Iowa State University

Title: Counting paths, cycles, and other subgraphs in planar graphs

Abstract: For a planar graph H, let N_P(n,H) denote the maximum number of copies of H in an n-vertex planar graph. The case where H is the path on 3 vertices, H=P_3, was established by Alon and Caro. The case of H=P_4 was determined, also exactly, by Gy\H{o}ri, Paulos, Salia, Tompkins, and Zamora. In this talk, we will give the asymptotic values for H equal to P_5 and P_7 as well as the cycles C_6, C_8, C_{10} and C_{12} and discuss the general approach which can be used to compute the asymptotic value for many other graphs H.