## April 2022

### Jakub Gajarský, Model Checking on Interpretations of Classes of Bounded Local Clique-Width

Zoom ID: 869 4632 6610 (ibsdimag)

The first-order model checking problem for finite graphs asks, given a graph G and a first-order sentence $\phi$ as input, to decide whether $\phi$ holds on G. Showing the existence of an efficient algorithm for this problem implies the existence of efficient parameterized algorithms for various commonly studied problems, such as independent set, distance-r dominating

### Michael Savery, Induced subgraphs of induced subgraphs of large chromatic number

Zoom ID: 869 4632 6610 (ibsdimag)

We prove that for every graph F with at least one edge there are graphs H of arbitrarily large chromatic number and the same clique number as F such that every F-free induced subgraph of H has chromatic number at most c=c(F). (Here a graph is F-free if it does not contain an induced copy

## May 2022

### Jan Kurkofka, Canonical Graph Decompositions via Coverings

Zoom ID: 869 4632 6610 (ibsdimag)

We present a canonical way to decompose finite graphs into highly connected local parts. The decomposition depends only on an integer parameter whose choice sets the intended degree of locality. The global structure of the graph, as determined by the relative position of these parts, is described by a coarser model. This is a simpler

### Sebastian Siebertz, Transducing paths in graph classes with unbounded shrubdepth

Zoom ID: 869 4632 6610 (ibsdimag)

Transductions are a general formalism for expressing transformations of graphs (and more generally, of relational structures) in logic. We prove that a graph class C can be FO-transduced from a class of bounded-height trees (that is, has bounded shrubdepth) if, and only if, from C one cannot FO-transduce the class of all paths. This establishes

## June 2022

### Jeck Lim, Sums of linear transformations

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

We show that if $L_1$ and $L_2$ are linear transformations from $\mathbb{Z}^d$ to $\mathbb{Z}^d$ satisfying certain mild conditions, then, for any finite subset $A$ of $\mathbb{Z}^d$, \ This result corrects and confirms the two-summand case of a conjecture of Bukh and is best possible up to the lower-order term for many choices of $L_1$ and

### Chengfei Xie, On the packing densities of superballs in high dimensions

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

The sphere packing problem asks for the densest packing of nonoverlapping equal-sized balls in the space. This is an old and difficult problem in discrete geometry. In this talk, we give a new proof for the result that for $1<p<2$, the translative packing density of superballs (a generalization of $\ell^p$ balls) in $\mathbb{R}^n$

### Xizhi Liu, Hypergraph Turán problem: from 1 to ∞

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

One interesting difference between (nondegenerate) Graph Turán problem and Hypergraph Turán problem is that the hypergraph families can have at least two very different extremal constructions. In this talk, we will look at some recent progress and approaches to constructing hypergraph families with at least two different extremal constructions. Based on some joint work with

## July 2022

### Sepehr Hajebi, Holes, hubs and bounded treewidth

Zoom ID: 869 4632 6610 (ibsdimag)

A hole in a graph $G$ is an induced cycle of length at least four, and for every hole $H$ in $G$, a vertex $h\in G\setminus H$ is called a $t$-hub for $H$ if $h$ has at least $t$ neighbor in $H$. Sintiari and Trotignon were the first to construct graphs with arbitrarily large treewidth

### Noam Lifshitz, Product free sets in the alternating group

Zoom ID: 870 0312 9412 (ibsecopro) [CLOSED]

A subset of a group is said to be product free if it does not contain the product of two elements in it. We consider how large can a product free subset of $A_n$ be? In the talk we will completely solve the problem by determining the largest product free subset of $A_n$. Our proof

## August 2022

### Lars Jaffke, Taming graphs with no large creatures and skinny ladders

Zoom ID: 869 4632 6610 (ibsdimag)

We confirm a conjecture of Gartland and Lokshtanov : if for a hereditary graph class $\mathcal{G}$ there exists a constant $k$ such that no member of $\mathcal{G}$ contains a $k$-creature as an induced subgraph or a $k$-skinny-ladder as an induced minor, then there exists a polynomial $p$ such that every $G \in \mathcal{G}$ contains at

기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209