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 2022Show all

4 papers · 1 filter

math.CO2022

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs

Alexandr Kostochka, Ruth Luo, Grace McCourt

Dirac proved that each $n$ -vertex $2$ -connected graph with minimum degree at least $k$ contains a cycle of length at least $min {2 k, n}$ . We consider a hypergraph version of this…

math.CO2022

On a property of $2$ -connected graphs and Dirac's Theorem

Alexandr Kostochka, Ruth Luo, Grace McCourt

We refine a property of $2$ -connected graphs described in the classical paper of Dirac from 1952 and use the refined property to somewhat shorten Dirac's proof of the fact that eac…

math.CO2022

Minimum degree ensuring that a hypergraph is hamiltonian-connected

Alexandr Kostochka, Ruth Luo, Grace McCourt

A hypergraph $H$ is hamiltonian-connected if for any distinct vertices $x$ and $y$ , $H$ contains a hamiltonian Berge path from $x$ to $y$ . We find for all $3 \leq r < n$ , exact lower…

math.CO2022

Saturation for the $3$ -uniform loose $3$ -cycle

Sean English, Alexandr Kostochka, Dara Zirlin

Let $F$ and $H$ be $k$ -uniform hypergraphs. We say $H$ is $F$ -saturated if $H$ does not contain a subgraph isomorphic to $F$ , but $H + e$ does for any hyperedge $e \neq \in E (H)$ . The…

A hypergraph analog of Dirac's Theorem for long cycles in 2-connected graphs

On a property of 2-connected graphs and Dirac's Theorem

Minimum degree ensuring that a hypergraph is hamiltonian-connected

Saturation for the 3-uniform loose 3-cycle

On a property of $2$ -connected graphs and Dirac's Theorem

Saturation for the $3$ -uniform loose $3$ -cycle