Hugo Jacob, On the parameterized complexity of computing tree-partitions

Zoom ID: 869 4632 6610 (ibsdimag)

Following some recent FPT algorithms parameterized by the width of a given tree-partition due to Bodlaender, Cornelissen, and van der Wegen, we consider the parameterized problem of computing a decomposition. We prove that computing an optimal tree-partition is XALP-complete, which is likely to exclude FPT algorithms. However, we prove that computing a tree-partition of approximate

Sebastian Wiederrecht, Excluding single-crossing matching minors in bipartite graphs

Room B332 IBS (기초과학연구원)

By a seminal result of Valiant, computing the permanent of (0, 1)-matrices is, in general, #P-hard. In 1913 Pólya asked for which (0, 1)-matrices A it is possible to change some signs such that the permanent of A equals the determinant of the resulting matrix. In 1975, Little showed these matrices to be exactly the

Chong Shangguan (上官冲), On the sparse hypergraph problem of Brown, Erdős and Sós

Zoom ID: 224 221 2686 (ibsecopro)

For fixed integers $r\ge 3, e\ge 3$, and $v\ge r+1$, let $f_r(n,v,e)$ denote the maximum number of edges in an $n$-vertex $r$-uniform hypergraph in which the union of arbitrary $e$ distinct edges contains at least $v+1$ vertices. In 1973, Brown, Erdős and Sós initiated the study of the function $f_r(n,v,e)$ and they proved that $\Omega(n^{\frac{er-v}{e-1}})=f_r(n,v,e)=O(n^{\lceil\frac{er-v}{e-1}\rceil})$.

Seonghyuk Im (임성혁), A proof of the Elliott-Rödl conjecture on hypertrees in Steiner triple systems

Room B332 IBS (기초과학연구원)

A linear $3$-graph is called a (3-)hypertree if there exists exactly one path between each pair of two distinct vertices.  A linear $3$-graph is called a Steiner triple system if each pair of two distinct vertices belong to a unique edge. A simple greedy algorithm shows that every $n$-vertex Steiner triple system $G$ contains all

Cosmin Pohoata, Convex polytopes from fewer points

Zoom ID: 224 221 2686 (ibsecopro)

Finding the smallest integer $N=ES_d(n)$ such that in every configuration of $N$ points in $\mathbb{R}^d$ in general position, there exist $n$ points in convex position is one of the most classical problems in extremal combinatorics, known as the Erdős-Szekeres problem. In 1935, Erdős and Szekeres famously conjectured that $ES_2(n)=2^{n−2}+1$ holds, which was nearly settled by

Giannos Stamoulis, Model-Checking for First-Order Logic with Disjoint Paths Predicates in Proper Minor-Closed Graph Classes

Room B332 IBS (기초과학연구원)

The disjoint paths logic, FOL+DP,  is an extension of First Order Logic (FOL) with the extra atomic predicate $\mathsf{dp}_k(x_1,y_1,\ldots,x_k,y_k),$ expressing the existence of internally vertex-disjoint paths between $x_i$ and $y_i,$ for $i\in \{1,\ldots, k\}$. This logic can express a wide variety of problems that escape the expressibility potential of FOL. We prove that for every

Maya Sankar, Homotopy and the Homomorphism Threshold of Odd Cycles

Zoom ID: 224 221 2686 (ibsecopro)

Fix $r \ge 2$ and consider a family F of $C_{2r+1}$-free graphs, each having minimum degree linear in its number of vertices. Such a family is known to have bounded chromatic number; equivalently, each graph in F is homomorphic to a complete graph of bounded size. We disprove the analogous statement for homomorphic images that

Stijn Cambie, The 69-conjecture and more surprises on the number of independent sets

Room B332 IBS (기초과학연구원)

Various types of independent sets have been studied for decades. As an example, the minimum number of maximal independent sets in a connected graph of given order is easy to determine (hint; the answer is written in the stars). When considering this question for twin-free graphs, it becomes less trivial and one discovers some surprising

Youngho Yoo (유영호), Approximating TSP walks in subcubic graphs

Room B332 IBS (기초과학연구원)

The Graphic Travelling Salesman Problem is the problem of finding a spanning closed walk (a TSP walk) of minimum length in a given connected graph. The special case of the Graphic TSP on subcubic graphs has been studied extensively due to their worst-case behaviour in the famous $\frac{4}{3}$-integrality-gap conjecture on the "subtour elimination" linear programming

Mamadou Moustapha Kanté, MSOL-Definable decompositions

Room B332 IBS (기초과학연구원)

I will first introduce the notion of recognisability of languages of terms and then its extensions to sets of relational structures. In a second step, I will discuss relations with decompositions of graphs/matroids and why their MSOL-definability is related to understanding recognisable sets. I will finally explain  how to define in MSOL branch-decompositions for finitely

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