Raphael Steiner, Congruence-constrained subdivisions in digraphs
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 …
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 …
We introduce a novel definition of orientation on the triples of a family of pairwise intersecting planar convex sets and study its properties. In particular, we compare it to other …
An $n$-vertex graph is called $C$-Ramsey if it has no clique or independent set of size $C\log_2 n$ (i.e., if it has near-optimal Ramsey behavior). We study edge-statistics in Ramsey …
A common technique to characterize hereditary graph classes is to exhibit their minimal obstructions. Sometimes, the set of minimal obstructions might be infinite, or too complicated to describe. For instance, for any …
A well-known conjecture of Burr and Erdős asserts that the Ramsey number $r(Q_n)$ of the hypercube $Q_n$ on $2^n$ vertices is of the order $O(2^n)$. In this paper, we show that …
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. …
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 $e$ …
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 …
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 …
Distributed certification, whether it be proof-labeling schemes, locally checkable proofs, etc., deals with the issue of certifying the legality of a distributed system with respect to a given boolean predicate. A certificate …