Department of Mathematics Calendar

Back to Listing

The Department of Mathematics Calendar has moved to Webtools. Anyone may submit an event by clicking the "+" button (upper right). Note: the Sponsor field is required. Just type "n/a"

All events will be reviewed before acceptance. Please email Shelby Koehne if you have any questions about submitting an event.

Note: you may search past and future events by clicking on the magnifying glass icon on the main Calendar page.

For an archive of past events: https://math.illinois.edu/research/seminars-department-calendar

Graph Theory and Combinatorics Seminar: The Turán number of Berge book hypergraphs

Event Type
Seminar/Symposium
Sponsor
N/A
Location
Zoom
Date
Feb 15, 2022   1:00 pm  
Speaker
Dániel Gerbner (Renyi Institute)
Contact
Sean English
Views
11
Given a graph G, a Berge copy of G is a hypergraph obtained by enlarging the edges arbitrarily. Gyori in 2006 showed that for r=3 or r=4, an r-uniform n-vertex Berge triangle-free hypergraph has at most floor[n^2/8(r-2)] hyperedges if n is large enough, and this bound is sharp.

The book graph B_t consists of t triangles sharing an edge. Very recently, Ghosh, Győri, Nagy-György, Paulos, Xiao and Zamora showed that a 3-uniform n-vertex Berge B_t-free hypergraph has at most n^2/8+o(n^2) hyperedges if n is large enough. They conjectured that this bound can be improved to floor[n^2/8].We prove this conjecture for t=2 and disprove it for t>2 by proving the sharp bound floor[n^2/8]+(t-1)^2. We also consider larger uniformity and determine the largest number of Berge B_t-free r-uniform hypergraphs besides an additive term o(n^2). We obtain a similar bound if the Berge t-fan (t triangles sharing a vertex) is forbidden.

For Zoom information please contact Sean at SEnglish (at) illinois (dot) edu.

link for robots only