Huy Tuan Pham, Random Cayley graphs and Additive combinatorics without groups

Room B332 IBS (기초과학연구원)

A major goal of additive combinatorics is to understand the structures of subsets A of an abelian group G which has a small doubling K = |A+A|/|A|. Freiman's celebrated theorem first provided a structural characterization of sets with small doubling over the integers, and subsequently Ruzsa in 1999 proved an analog for abelian groups with

Tony Huynh, The Peaceable Queens Problem

Room B332 IBS (기초과학연구원)

The peaceable queens problem asks to determine the maximum number $a(n)$ such that there is a placement of $a(n)$ white queens and $a(n)$ black queens on an $n \times n$ chessboard so that no queen can capture any queen of the opposite color. We consider the peaceable queens problem and its variant on the toroidal

Laure Morelle, Bounded size modifications in time $2^{{\sf poly}(k)}\cdot n^2$

Room B332 IBS (기초과학연구원)

A replacement action is a function $\mathcal L$ that maps each graph to a collection of subgraphs of smaller size. Given a graph class $\mathcal H$, we consider a general family of graph modification problems, called "$\mathcal L$-Replacement to $\mathcal H$", where the input is a graph $G$ and the question is whether it is

Jungho Ahn (안정호), A coarse Erdős-Pósa theorem for constrained cycles

Room B332 IBS (기초과학연구원)

An induced packing of cycles in a graph is a set of vertex-disjoint cycles such that the graph has no edge between distinct cycles of the set. The classic Erdős-Pósa theorem shows that for every positive integer $k$, every graph contains $k$ vertex-disjoint cycles or a set of $O(k\log k)$ vertices which intersects every cycle of $G$.

O-joung Kwon (권오정), Erdős-Pósa property of A-paths in unoriented group-labelled graphs

Room B332 IBS (기초과학연구원)

A family $\mathcal{F}$ of graphs is said to satisfy the Erdős-Pósa property if there exists a function $f$ such that for every positive integer $k$, every graph $G$ contains either $k$ (vertex-)disjoint subgraphs in $\mathcal{F}$ or a set of at most $f(k)$ vertices intersecting every subgraph of $G$ in $\mathcal{F}$. We characterize the obstructions to

Sepehr Hajebi, The pathwidth theorem for induced subgraphs

Room B332 IBS (기초과학연구원)

We present a full characterization of the unavoidable induced subgraphs of graphs with large pathwidth. This consists of two results. The first result says that for every forest H, every graph of sufficiently large pathwidth contains either a large complete subgraph, a large complete bipartite induced minor, or an induced minor isomorphic to H. The

Irene Muzi, An elementary bound for Younger’s conjecture

Room B332 IBS (기초과학연구원)

In 1996, Reed, Robertson, Seymour and Thomas proved Younger's Conjecture, which states that for all directed graphs D, there exists a function f such that if D does not contain k disjoint cycles, D contains a feedback vertex set, i.e. a subset of vertices whose deletion renders the graph acyclic, of size bounded by f(k).

Johannes Carmesin, Open problems in graph theory

Room B332 IBS (기초과학연구원)

Since the proof of the graph minor structure theorem by Robertson and Seymour in 2004, its underlying ideas have found applications in a much broader range of settings than their original context. They have driven profound progress in areas such as vertex minors, pivot minors, matroids, directed graphs, and 2-dimensional simplicial complexes. In this talk,

Michał Seweryn, Dimension and standard examples in planar posets

Room B332 IBS (기초과학연구원)

The dimension of a poset is the least integer $d$ such that the poset is isomorphic to a subposet of the product of $d$ linear orders. In 1983, Kelly constructed planar posets of arbitrarily large dimension. Crucially, the posets in his construction involve large standard examples, the canonical structure preventing a poset from having small

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