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

Seunghun Lee (이승훈), Inscribable order types

Room B332 IBS (기초과학연구원)

We call an order type inscribable if it is realized by a point configuration where all extreme points are all on a circle. In this talk, we investigate inscribability of order types. We first show that every simple order type with at most 2 interior points is inscribable, and that the number of such order

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

Eun Jung Kim (김은정), Directed flow-augmentation

Room B332 IBS (기초과학연구원)

We show a flow-augmentation algorithm in directed graphs: There exists a polynomial-time algorithm that, given a directed graph G, two integers $s,t\in V(G)$, and an integer $k$, adds (randomly) to $G$ a number of arcs such that for every minimal st-cut $Z$ in $G$ of size at most $k$, with probability $2^{−\operatorname{poly}(k)}$ the set $Z$

Akash Kumar, Random walks and Forbidden Minors

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

Random walks and spectral methods have had a strong influence on modern graph algorithms as evidenced by the extensive literature on the subject. In this talk, I will present how random walks helped make progress on algorithmic problems on planar graphs. In particular, I show how random walk based (i.e., spectral) approaches led to progress

Noleen Köhler, Testing first-order definable properties on bounded degree graphs

Room B332 IBS (기초과학연구원)

Property testers are probabilistic algorithms aiming to solve a decision problem efficiently in the context of big-data. A property tester for a property P has to decide (with high probability correctly) whether a given input graph has property P or is far from having property P while having local access to the graph. We study

Raul Lopes, Temporal Menger and related problems

Room B332 IBS (기초과학연구원)

A temporal graph is a graph whose edges are available only at specific times. In this scenario, the only valid walks are the ones traversing adjacent edges respecting their availability, i.e. sequence of adjacent edges whose appearing times are non-decreasing. Given a graph G and vertices s and t of G, Menger’s Theorem states that

Brett Leroux, Expansion of random 0/1 polytopes

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

A conjecture of Milena Mihail and Umesh Vazirani states that the edge expansion of the graph of every $0/1$ polytope is at least one. Any lower bound on the edge expansion gives an upper bound for the mixing time of a random walk on the graph of the polytope. Such random walks are important because they can be used

Jun Gao, Number of (k-1)-cliques in k-critical graph

Room B332 IBS (기초과학연구원)

We prove that for $n>k\geq 3$, if $G$ is an $n$-vertex graph with chromatic number $k$ but any its proper subgraph has smaller chromatic number, then $G$ contains at most $n-k+3$ copies of cliques of size $k-1$. This answers a problem of Abbott and Zhou and provides a tight bound on a conjecture of Gallai.

Raphael Steiner, Congruence-constrained subdivisions in digraphs

Zoom ID: 869 4632 6610 (ibsdimag)

I will present the short proof from that for every digraph F and every assignment of pairs of integers $(r_e,q_e)_{e\in A(F)}$ to its arcs, there exists an integer $N$ such that every digraph D with dichromatic number at least $N$ contains a subdivision of $F$ in which $e$ is subdivided into a directed path of

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