Graph Theory & Combinatorics Seminar

Event Type

Seminar/Symposium

Sponsor

Department of Mathematics

Location

Altgeld 241

Date

Oct 11, 2022   1:00 pm  

Speaker

Alexandr Kostochka

Views

3

Alexandr Kostochka (UIUC)

On (1,2)-paths in 3-uniform hypergraphs

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Abstract: This is the second part of the talk on October 4. Recall that an (a,b)-path of length k is an (a+b)-uniform hypergraph P_k(a,b) defined as follows: V(P_k(a,b)) consists of k+1 sets A_1,...,A_{k+1} with |A_1|=|A_3|=...=a and |A_2|=|A_4|=...=b, and E(P_k(a,b))={A_i\cup A_{i+1}: 1 \leq i \leq k}.

 

In this part, we use the Delta-systems method to prove that the maximum number of edges in a 3-uniform n-vertex hypergraph not containing

P_{4}(1,2) is {n-1 \choose 2} + O(n).

 

This is joint work with Z. Füredi, T. Jiang, D. Mubayi, and J. Verstraëte.