Extremal and Probabilistic Combinatorics (2021 KMS Spring Meeting)

A special session "Extremal and Probabilistic Combinatorics" at the 2021 KMS Spring Meeting is organized by Tuan Tran. URL: https://www.kms.or.kr/meetings/spring2021/ Speakers and Schedule All talks are on April 30. Joonkyung Lee (이준경), University College London Majority dynamics on sparse random graphs Dong Yeap Kang (강동엽), Unversity of Birmingham The Erdős-Faber-Lovász conjecture and related results  Jinyoung

Raul Lopes, Adapting the Directed Grid Theorem into an FPT Algorithm

Zoom ID: 869 4632 6610 (ibsdimag)

The Grid Theorem of Robertson and Seymour is one of the most important tools in the field of structural graph theory, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem in digraphs was conjectured by Johnson et al. , and proved by Kawarabayashi and Kreutzer .

Hong Liu, Sublinear expander and embeddings sparse graphs

Zoom

A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory, including e.g. the odd cycle problem of Erdős and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some

Mark Siggers, The list switch homomorphism problem for signed graphs

Room B232 IBS (기초과학연구원)

A signed graph is a graph in which each edge has a positive or negative sign. Calling two graphs switch equivalent if one can get from one to the other by the iteration of the local action of switching all signs on edges incident to a given vertex, we say that there is a switch

Johannes Carmesin, A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings

Zoom ID: 869 4632 6610 (ibsdimag)

Given a graph, how do we construct a surface so that the graph embeds in that surface in an optimal way? Thomassen showed that for minimum genus as optimality criterion, this problem would be NP-hard. Instead of minimum genus, here we use local planarity -- and provide a polynomial algorithm. Our embedding method is based

Pascal Gollin, Enlarging vertex-flames in countable digraphs

Room B232 IBS (기초과학연구원)

A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means

Benjamin Bumpus, Directed branch-width: A directed analogue of tree-width

Zoom ID: 869 4632 6610 (ibsdimag)

Many problems that are NP-hard in general become tractable on `structurally recursive’ graph classes. For example, consider classes of bounded tree- or clique-width. Since the 1990s, many directed analogues of tree-width have been proposed. However, many natural problems (e.g. directed HamiltonPath and MaxCut) remain intractable on such digraph classes of `bounded width’. In this talk,

Ben Lund, Limit shape of lattice Zonotopes

Room B232 IBS (기초과학연구원)

A convex lattice polytope is the convex hull of a set of integral points. Vershik conjectured the existence of a limit shape for random convex lattice polygons, and three proofs of this conjecture were given in the 1990s by Bárány, by Vershik, and by Sinai. To state this old result more precisely, there is a

Dimitrios M. Thilikos, Bounding Obstructions sets: the cases of apices of minor closed classes

Zoom ID: 869 4632 6610 (ibsdimag)

Given a minor-closed graph class ${\cal G}$, the (minor) obstruction of ${\cal G}$ is the set of all minor-minimal graphs not in ${\cal G}$. Given a non-negative integer $k$, we define the $k$-apex of ${\cal A}$ as the class containing every graph $G$ with a set $S$ of vertices whose removal from $G$ gives a graph

Doowon Koh (고두원), Mattila-Sjölin type functions: A finite field model

Room B232 IBS (기초과학연구원)

Let $\mathbb{F}_q$ be a finite field of order $q$ which is a prime power. In the finite field setting, we say that a function $\phi\colon \mathbb{F}_q^d\times \mathbb{F}_q^d\to \mathbb{F}_q$ is a Mattila-Sjölin type function in $\mathbb{F}_q^d$ if for any $E\subset \mathbb{F}_q^d$ with $|E|\gg q^{\frac{d}{2}}$, we have $\phi(E, E)=\mathbb{F}_q$. The main purpose of this talk is to present

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