Dara Zirlin

activity

20182023

2 ℓ + 1

vertices are

ℓ

-recognizable

2 citations · 2 across the 5 of their papers we have counts for

collaborators

Showing math.COShow all

10 papers · 1 filter

math.CO2023

Acyclic graphs with at least $2 ℓ + 1$ vertices are $ℓ$ -recognizable

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West +1

The $(n - ℓ)$ -deck of an $n$ -vertex graph is the multiset of subgraphs obtained from it by deleting $ℓ$ vertices. A family of $n$ -vertex graphs is $ℓ$ -recognizable if every…

math.CO2023

Trees with at least $6 ℓ + 11$ vertices are $ℓ$ -reconstructible

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West +1

The $(n - ℓ)$ -deck of an $n$ -vertex graph is the multiset of (unlabeled) subgraphs obtained from it by deleting $ℓ$ vertices. An $n$ -vertex graph is $ℓ$ -reconstructible if i…

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…

math.CO2021★ 2 cited

Acyclic graphs with at least $2 ℓ + 1$ vertices are $ℓ$ -recognizable

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West +1

The $(n - ℓ)$ -deck of an $n$ -vertex graph is the multiset of subgraphs obtained from it by deleting $ℓ$ vertices. A family of $n$ -vertex graphs is $ℓ$ -recognizable if every…

math.CO2020

Conditions for a bigraph to be super-cyclic

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo +1

A hypergraph $H$ is super-pancyclic if for each $A \subseteq V (H)$ with $∣ A ∣ \geq 3$ , $H$ contains a Berge cycle with base vertex set $A$ . We present two…

math.CO2020

Longest cycles in 3-connected hypergraphs and bipartite graphs

Alexandr Kostochka, Mikhail Lavrov, Ruth Luo +1

In the language of hypergraphs, our main result is a Dirac-type bound: we prove that every $3$ -connected hypergraph $H$ with $δ (H) \geq max {∣ V (H) ∣, \frac{∣ E ( H ) ∣ + 10}{4}}$ has a h…

math.CO2019

3-Regular Graphs Are 2-Reconstructible

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West +1

A graph is $ℓ$ -reconstructible if it is determined by its multiset of induced subgraphs obtained by deleting $ℓ$ vertices. We prove that $3$ -regular graphs are $2$ -reconstruc…

math.CO2019

Super-pancyclic hypergraphs and bipartite graphs

Alexandr Kostochka, Ruth Luo, Dara Zirlin

We find Dirac-type sufficient conditions for a hypergraph $H$ with few edges to be hamiltonian. We also show that these conditions provide that $H$ is {\em super-…

math.CO2019

Degree lists and connectedness are $3$ -reconstructible for graphs with at least seven vertices

Alexandr V. Kostochka, Mina Nahvi, Douglas B. West +1

The $k$ -deck of a graph is the multiset of its subgraphs induced by $k$ vertices. A graph or graph property is $l$ -reconstructible if it is determined by the deck of subgraphs obta…

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…

Acyclic graphs with at least 2ℓ+1 vertices are ℓ-recognizable

Trees with at least 6ℓ+11 vertices are ℓ-reconstructible

Saturation for the 3-uniform loose 3-cycle

Acyclic graphs with at least 2ℓ+1 vertices are ℓ-recognizable

Conditions for a bigraph to be super-cyclic

Longest cycles in 3-connected hypergraphs and bipartite graphs

3-Regular Graphs Are 2-Reconstructible

Super-pancyclic hypergraphs and bipartite graphs

Degree lists and connectedness are 3-reconstructible for graphs with at least seven vertices

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

Acyclic graphs with at least $2 ℓ + 1$ vertices are $ℓ$ -recognizable

Trees with at least $6 ℓ + 11$ vertices are $ℓ$ -reconstructible

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

Acyclic graphs with at least $2 ℓ + 1$ vertices are $ℓ$ -recognizable

Degree lists and connectedness are $3$ -reconstructible for graphs with at least seven vertices