B. Bukh

activity

20072026

most citedA bound on the number of edges in graphs without an even cycle

61 citations · 249 across the 42 of their papers we have counts for

collaborators

Showing 2020 · math.COShow all

3 papers · 2 filters

math.CO2020★ 3 cited

Empty axis-parallel boxes

Boris Bukh, Ting-Wei Chao

We show that, for every set of $n$ points in the $d$ -dimensional unit cube, there is an empty axis-parallel box of volume at least $Ω (d / n)$ as $n \to \infty$ and $d$ is fixed. In the…

math.CO2020★ 4 cited

On convex holes in $d$ -dimensional point sets

Boris Bukh, Ting-Wei Chao, Ron Holzman

Given a finite set $A \subseteq R^{d}$ , points $a_{1}, a_{2}, \dots, a_{ℓ} \in A$ form an $ℓ$ -hole in $A$ if they are the vertices of a convex polytope which contains no poi…

math.CO2020

Order-isomorphic twins in permutations

Boris Bukh, Oleksandr Rudenko

Let $a_{1}, \dots, a_{n}$ be a permutation of $[n]$ . Two disjoint order-isomorphic subsequences are called \emph{twins}. We show that every permutation of $[n]$ contains twins of length…

Empty axis-parallel boxes

On convex holes in d-dimensional point sets

Order-isomorphic twins in permutations

On convex holes in $d$ -dimensional point sets