A. Kostochka

activity

20052023

most citedDP-colorings of graphs with high chromatic number

42 citations · 275 across the 72 of their papers we have counts for

collaborators

Showing 2018Show all

10 papers · 1 filter

math.CO2018★ 14 cited

Avoiding long Berge cycles II, exact bounds for all $n$

Zoltan Furedi, Alexandr Kostochka, Ruth Luo

Let $E G_{r} (n, k)$ denote the maximum number of edges in an $n$ -vertex $r$ -uniform hypergraph with no Berge cycles of length $k$ or longer. In the first part of this work, we have fou…

math.CO2018★ 3 cited

Extremal problems on ordered and convex geometric hypergraphs

Zoltán Füredi, Tao Jiang, Alexandr Kostochka +2

An ordered hypergraph is a hypergraph whose vertex set is linearly ordered, and a convex geometric hypergraph is a hypergraph whose vertex set is cyclically ordered. Extremal probl…

math.CO2018★ 19 cited

On $r$ -uniform hypergraphs with circumference less than $r$

Alexandr Kostochka, Ruth Luo

We show that for each $k \geq 4$ and $n > r \geq k + 1$ , every $n$ -vertex $r$ -uniform hypergraph with no Berge cycle of length at least $k$ has at most $\frac{( k - 1 ) ( n - 1 )}{r}$ edges. The…

math.CO2018

DP-Colorings of Hypergraphs

Anton Bernshteyn, Alexandr Kostochka

Classical problems in hypergraph coloring theory are to estimate the minimum number of edges, $m_{2} (r)$ (respectively, $m_{2}^{*} (r)$ ), in a non- $2$ -colorable $r$ -uniform (respective…

math.CO2018

Hypergraphs not containing a tight tree with a bounded trunk ~II: 3-trees with a trunk of size 2

Zoltán Füredi, Tao Jiang, Alexandr Kostochka +2

A tight $r$ -tree $T$ is an $r$ -uniform hypergraph that has an edge-ordering $e_{1}, e_{2}, \dots, e_{t}$ such that for each $i \geq 2$ , $e_{i}$ has a vertex $v_{i}$ that does not belong to an…

math.CO2018

Cut-edges and regular factors in regular graphs of odd degree

Alexander V. Kostochka, André Raspaud, Bjarne Toft +2

We study $2 k$ -factors in $(2 r + 1)$ -regular graphs. Hanson, Loten, and Toft proved that every $(2 r + 1)$ -regular graph with at most $2 r$ cut-edges has a $2$ -factor. We generalize their…

Avoiding long Berge cycles II, exact bounds for all n

Extremal problems on ordered and convex geometric hypergraphs

On r-uniform hypergraphs with circumference less than r

DP-Colorings of Hypergraphs

Hypergraphs not containing a tight tree with a bounded trunk ~II: 3-trees with a trunk of size 2

Cut-edges and regular factors in regular graphs of odd degree

Avoiding long Berge cycles II, exact bounds for all $n$

On $r$ -uniform hypergraphs with circumference less than $r$