Sebastian Wiederrecht, Packing even directed circuits quarter-integrally

Room B332 IBS (기초과학연구원)

We prove the existence of a computable function $f\colon\mathbb{N}\to\mathbb{N}$ such that for every integer $k$ and every digraph $D$ either contains a collection $\mathcal{C}$ of $k$ directed cycles of even length such that no vertex of $D$ belongs to more than four cycles in $\mathcal{C}$, or there exists a set $S\subseteq V(D)$ of size at

Jie Han (韩杰), Perfect matchings in dense uniform hypergraphs

Room B332 IBS (기초과학연구원)

There has been a raising interest on the study of perfect matchings in uniform hypergraphs in the past two decades, including extremal problems and their algorithmic versions. I will introduce the problems and some recent developments.

Linda Cook, On polynomial degree-boundedness

Room B332 IBS (기초과학연구원)

We prove a conjecture of Bonamy, Bousquet, Pilipczuk, Rzążewski, Thomassé, and Walczak, that for every graph $H$, there is a polynomial $p$ such that for every positive integer $s$, every graph of average degree at least $p(s)$ contains either $K_{s,s}$ as a subgraph or contains an induced subdivision of $H$. This improves upon a result

Evangelos Protopapas, Erdős-Pósa Dualities for Minors

Room B332 IBS (기초과학연구원)

Let $\mathcal{G}$ and $\mathcal{H}$ be minor-closed graphs classes. The class $\mathcal{H}$ has the Erdős-Pósa property in $\mathcal{G}$ if there is a function $f : \mathbb{N} \to \mathbb{N}$ such that every graph $G$ in $\mathcal{G}$ either contains (a packing of) $k$ disjoint copies of some subgraph minimal graph $H \not\in \mathcal{H}$ or contains (a covering of)

Casey Tompkins, On graphs without cycles of length 0 modulo 4

Room B332 IBS (기초과학연구원)

Bollobás proved that for every $k$ and $\ell$ such that $k\mathbb{Z}+\ell$ contains an even number, an $n$-vertex graph containing no cycle of length $\ell \bmod k$ can contain at most a linear number of edges. The precise (or asymptotic) value of the maximum number of edges in such a graph is known for very few

Eero Räty, Positive discrepancy, MaxCut and eigenvalues of graphs

Room B332 IBS (기초과학연구원)

The positive discrepancy of a graph $G$ of edge density $p$ is defined as the maximum of $e(U) - p|U|(|U|-1)/2$, where the maximum is taken over subsets of vertices in G. In 1993 Alon proved that if G is a $d$-regular graph on $n$ vertices and $d = O(n^{1/9})$, then the positive discrepancy of $G$

Magnus Wahlström, Algorithmic aspects of linear delta-matroids

Room B332 IBS (기초과학연구원)

Delta-matroids are a generalization of matroids with connections to many parts of graph theory and combinatorics (such as matching theory and the structure of topological graph embeddings). Formally, a delta-matroid is a pair $D=(V,\mathcal F)$ where $\mathcal F$ is a collection of subsets of V known as "feasible sets." (They can be thought of as

Víctor Dalmau, Right-adjoints of Datalog Programs

Room B332 IBS (기초과학연구원)

We say that two functors Λ and Γ between thin categories of relational structures are adjoint if for all structures A and B, we have that Λ(A) maps homomorphically to B if and only if A maps homomorphically to Γ(B). If this is the case Λ is called the left adjoint to Γ and Γ

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