Carla Groenland

activity

20182025

most citedExact hyperplane covers for subsets of the hypercube

5 citations · 15 across the 12 of their papers we have counts for

collaborators

16 papers

math.CO2025

Infinite induced-saturated graphs

Marthe Bonamy, Carla Groenland, Tom Johnston +2

A graph $G$ is $H$ -induced-saturated if $G$ is $H$ -free but deleting any edge or adding any edge creates an induced copy of $H$ . There are non-trivial graphs $H$ , such as $P_{4}$ , fo…

math.CO2023★ 3 cited

A Polynomial Upper Bound for Poset Saturation

Paul Bastide, Carla Groenland, Maria-Romina Ivan +1

Given a finite poset $P$ , we say that a family $F$ of subsets of $[n]$ is $P$ -saturated if $F$ does not contain an induced copy of $P$ ,…

math.CO2023★ 1 cited

Counting graphic sequences via integrated random walks

Paul Balister, Serte Donderwinkel, Carla Groenland +2

Given an integer $n$ , let $G (n)$ be the number of integer sequences $n - 1 \geq d_{1} \geq d_{2} \geq \dots \geq d_{n} \geq 0$ that are the degree sequence of some graph. We show that $G(n)=(c+o(1))…

math.CO2022

Perfect shuffling with fewer lazy transpositions

Carla Groenland, Tom Johnston, Jamie Radcliffe +1

A lazy transposition $(a, b, p)$ is the random permutation that equals the identity with probability $1 - p$ and the transposition $(a, b) \in S_{n}$ with probability $p$ . How long must a…

math.CO2022

Short reachability networks

Carla Groenland, Tom Johnston, Jamie Radcliffe +1

We investigate the following generalisation of permutation networks. We say a sequence $T = (T_{1}, \dots, T_{ℓ})$ of transpositions in $S_{n}$ forms a $t$ -reachability network if, for ev…

math.CO2022★ 2 cited

Exact antichain saturation numbers via a generalisation of a result of Lehman-Ron

Paul Bastide, Carla Groenland, Hugo Jacob +1

For given positive integers $k$ and $n$ , a family $F$ of subsets of ${1, \dots, n}$ is $k$ -antichain saturated if it does not contain an antichain of size $k$ , but adding…

math.CO2022

Decomposing random permutations into order-isomorphic subpermutations

Carla Groenland, Tom Johnston, Dániel Korándi +3

Two permutations $s$ and $t$ are $k$ -similar if they can be decomposed into subpermutations $s^{1}, \dots, s^{k}$ and $t^{1}, \dots, t^{k}$ such that $s^{i}$ is order-isomorphic to $t^{i}$ f…

math.CO2021★ 1 cited

The lengths for which bicrucial square-free permutations exist

Carla Groenland, Tom Johnston

A square is a factor $S = (S_{1}; S_{2})$ where $S_{1}$ and $S_{2}$ have the same pattern, and a permutation is said to be square-free if it contains no non-trivial squares. The permutatio…

math.CO2021

Reconstruction from smaller cards

Carla Groenland, Tom Johnston, Alex Scott +1

The $ℓ$ -deck of a graph $G$ is the multiset of all induced subgraphs of $G$ on $ℓ$ vertices. We say that a graph is reconstructible from its $ℓ$ -deck if no other graph has…

math.CO2021

Reconstructing the degree sequence of a sparse graph from a partial deck

Carla Groenland, Tom Johnston, Andrey Kupavskii +3

The deck of a graph $G$ is the multiset of cards ${G - v : v \in V (G)}$ . Myrvold (1992) showed that the degree sequence of a graph on $n \geq 7$ vertices can be reconstructed from any d…

math.CO2020★ 5 cited

Exact hyperplane covers for subsets of the hypercube

James Aaronson, Carla Groenland, Andrzej Grzesik +2

Alon and Füredi (1993) showed that the number of hyperplanes required to cover ${0, 1}^{n} ∖ {0}$ without covering $0$ is $n$ . We initiate the study of such exact hyperplan…

math.CO2019★ 1 cited

Cyclically covering subspaces in $F_{2}^{n}$

James Aaronson, Carla Groenland, Tom Johnston

A subspace of $F_{2}^{n}$ is called cyclically covering if every vector in $F_{2}^{n}$ has a cyclic shift which is inside the subspace. Let $h_{2} (n)$ denote the largest po…

math.CO2018

Intersection sizes of linear subspaces with the hypercube

Carla Groenland, Tom Johnston

We continue the study by Melo and Winter [arXiv:1712.01763, 2017] on the possible intersection sizes of a $k$ -dimensional subspace with the vertices of the $n$ -dimensional hypercub…

math.CO2018

Size reconstructibility of graphs

Carla Groenland, Hannah Guggiari, Alex Scott

The deck of a graph $G$ is given by the multiset of (unlabelled) subgraphs ${G - v : v \in V (G)}$ . The subgraphs $G - v$ are referred to as the cards of $G$ . Brown and Fenner recently s…

math.PR2018

Exceptional graphs for the random walk

Juhan Aru, Carla Groenland, Tom Johnston +3

If $W$ is the simple random walk on the square lattice $Z^{2}$ , then $W$ induces a random walk $W_{G}$ on any spanning subgraph $G\subset \mathbb…

cs.DM2018★ 2 cited

$H$ -colouring $P_{t}$ -free graphs in subexponential time

Carla Groenland, Karolina Okrasa, Pawel Rzążewski +3

A graph is called $P_{t}$ -free if it does not contain the path on $t$ vertices as an induced subgraph. Let $H$ be a multigraph with the property that any two distinct vertices share…

Infinite induced-saturated graphs

A Polynomial Upper Bound for Poset Saturation

Counting graphic sequences via integrated random walks

Perfect shuffling with fewer lazy transpositions

Short reachability networks

Exact antichain saturation numbers via a generalisation of a result of Lehman-Ron

Decomposing random permutations into order-isomorphic subpermutations

The lengths for which bicrucial square-free permutations exist

Reconstruction from smaller cards

Reconstructing the degree sequence of a sparse graph from a partial deck

Exact hyperplane covers for subsets of the hypercube

Cyclically covering subspaces in F2n​

Intersection sizes of linear subspaces with the hypercube

Size reconstructibility of graphs

Exceptional graphs for the random walk

H-colouring Pt​-free graphs in subexponential time

Cyclically covering subspaces in $F_{2}^{n}$

$H$ -colouring $P_{t}$ -free graphs in subexponential time