Carla Groenland

activity

20182025

collaborators

7 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.CO2020

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

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…