Department of

Mathematics


Seminar Calendar
for Graph Theory and Combinatorics Seminar events the year of Tuesday, January 19, 2021.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Tuesday, January 26, 2021

2:00 pm in Zoom,Tuesday, January 26, 2021

Coding Theory and Sidon Sequences

Zoltan Furedi (Renyi Institute for Mathematics)

Abstract: A sequence ${a_1, a_2,\dots, a_k}$ of integers is called a $B_2$ sequence if all the sums $a_i + a_j$, $1 \leq i \leq j \leq k$, are different. Let $F_2(n)$ be the maximum number of elements that can be selected from the set ${1,2,\dots,n}$ so as to form a $B_2$ sequence. Among others we give a new elementary proof for the result of Erdos and Turan (1941) that $F_2(n)= \sqrt{n} + O(n^{1/4})$.

Tuesday, February 2, 2021

2:00 pm in Zoom,Tuesday, February 2, 2021

Acyclic graphs with at least 2L + 1 vertices are L-recognizable

Dara Zirlin (UIUC)

Abstract: The $(n-L)$-deck of an $n$-vertex graph is the multiset of subgraphs obtained from it by deleting $L$ vertices. A family of $n$-vertex graphs is $L$-recognizable if every graph having the same $(n-L)$-deck as a graph in the family is also in the family. We prove that the family of $n$-vertex graphs having no cycles is $L$-recognizable when $n\geq 2L+1$ (except when $(n,L)=(5,2)$). It is already known that this fails when $n=2L$ and when $(n,L)=(5,2)$.

This is joint work with Alexandr V. Kostochka, Mina Nahvi, and Douglas B. West.

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

Tuesday, February 9, 2021

2:00 pm in Zoom,Tuesday, February 9, 2021

Maximum Number of Almost Similar Triangles in the Plane

Felix Clemen (UIUC)

Abstract: A triangle $T'$ is $\epsilon$-similar to another triangle $T$ if their angles pairwise differ by at most $\epsilon$. Given a triangle $T$, $\epsilon>0$ and a natural number $n$, Bárány and Füredi asked to determine the maximum number of triangles being $\epsilon$-similar to $T$ in a planar point set of size $n$. We determine this quantity for almost all triangles $T$ and sufficiently small $\epsilon$. Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof. This is joint work with József Balogh and Bernard Lidický.

Please contact Sean at SEnglish (at) illinois (dot) edu for Zoom information.

Tuesday, February 16, 2021

2:00 pm in Zoom,Tuesday, February 16, 2021

A proof of the Erdős–Faber–Lovász conjecture

Abhishek Methuku (University of Birmingham)

Abstract: The celebrated Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this talk, I will sketch a proof of this conjecture for every large n.

Joint work with D. Kang, T. Kelly, D. Kühn and D. Osthus.

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

Tuesday, February 23, 2021

2:00 pm in Zoom,Tuesday, February 23, 2021

The Feasible Region of Hypergraphs

Dhruv Mubayi (University of Illinois, Chicago)

Abstract: Many extremal hypergraph problems seek to maximize the number of edges subject to some local constraints. We aim to gain a more detailed understanding of such problems by studying the maximum subject to an additional global constraint, namely the size of the shadow. Put differently, we seek the pairs $(x,y)$ in the unit square such that there are $F$-free hypergraphs whose shadow density approaches $x$ and edge density approaches $y$. I will give some general results about the shape of this "feasible region" and also extend and improve some classical Turan-type results for particular choices of $F$. This is joint work with Xizhi Liu.

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