List of upcoming online seminars in discrete mathematics, combinatorics, and graph theory

Title: APPLICATION OF ZERO-SUM SETS IN MAGIC-TYPE AND ANTIMAGIC-TYPE GRAPH LABELING
by Sylwia Cichacz (AGH University in Cracow, Poland) as part of Combinatorics Today Series – ITB

Abstract
Let $(\Gamma,+)$ be an Abelian group. A subset $S$ of $\Gamma$ is called a \textit{zero-sum subset} if $\sum_{a\in S} a=0$. One of the key topics in zero-sum theory is the study of disjoint zero-sum subsets in $\Gamma$. This approach was inspired by Steiner triples research and started by Skolem. \\

Interestingly, certain magic-type and antimagic-type graph labelings are closely related to disjoint zero-sum subsets in $\Gamma$. In this talk, we will explore some of these connections.

A {\em replacement action} is a function $\cal L$ that maps each graph to a collection of subgraphs of smaller size.

Given a graph class $\cal H$, we consider a general family of graph modification problems, called {\sc $\cal L$-Replacement to $\cal H$}, where the input is a graph $G$ and the question is whether it is possible to replace some induced subgraph $H_1$ of $G$ on at most $k$ vertices by a graph $H_2$ in ${\cal L}(H_1)$ so that the resulting graph belongs to $\cal H$.

{\sc $\cal L$-Replacement to $\cal H$} can simulate many graph modification problems including vertex deletion, edge deletion/addition/edition/contraction, vertex identification, subgraph complementation, independent set deletion, (induced) matching deletion/contraction, etc.

We prove here that, for any minor-closed graph class $\cal H$ and for any action $\cal L$ that is hereditary, there is an algorithm that solves {\sc $\cal L$-Replacement to $\cal H$} in time $2^{{\sf poly}(k)}\cdot |V(G)|^2$, where ${\sf poly}$ is a polynomial whose degree depends on $\cal H$.

by Gaku Liu (UW) as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA

by Jacques Verstraete (UCSD) as part of UCLA Combinatorics Forum

Lecture held in UCLA Boelter hall, room 5436.

Abstract
The Ramsey number $r(s,t)$ denotes the minimum $N$ such that in any red-blue coloring of the edges of the complete graph $K_N$, there exists a red $K_s$ or a blue $K_t$. While the study of these quantities goes back almost one hundred years, to early papers of Ramsey and Erd\H{o}s and Szekeres, the long-standing conjecture of Erd\H{o}s that $r(s,t)$ has order of magnitude close to $t^{s – 1}$ as $t \rightarrow \infty$ remains open in general. It took roughly sixty years before the order of magnitude of $r(3,t)$ was determined by Jeong Han Kim, who showed $r(3,t)$ has order of magnitude $t^2/(\log t)$ as $t \rightarrow \infty$. In this talk, we discuss a variety of new techniques, including mention of the proof that for some constants $a,b > 0$ and $t \geq 2$,
\[ a\frac{t^3}{(\log t)^4} \leq r(4,t) \leq b\frac{t^3}{(\log t)^2},\]
as well as new progress on other Ramsey numbers, on Erd\H{o}s-Rogers functions, Ramsey minimal graphs, and on coloring hypergraphs.

Joint work in part with David Conlon, Sam Mattheus, and Dhruv Mubayi.

Coarse graph theory is an emerging research direction that aims to describe the global structure of graphs by ignoring their local structure. In this talk, I will present an overview of this area, highlighting both recent positive and negative developments. A key focus of this talk will be the notion of quasi-isometry and conditions under which graphs are quasi-isometric to graphs with bounded treewidth.

This talk is based on some recent joint works with Rutger Campbell, Maria Chudnowsky, James Davies, Marc Distel, Meike Hatzel, Freddie Illingworth, and Rose McCarty.

by TBA as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA

by TBA as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA

by Daoji Huang (IAS) as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA

by Shiyue Li (IAS) as part of UCLA Combinatorics Forum

Lecture held in MS 6221.
Abstract: TBA