Natasha Morrison

collaborators

4 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.CO2025

Perfect tilings of 3-graphs with the generalised triangle

Candida Bowtell, Amarja Kathapurkar, Natasha Morrison +1

We establish a best-possible minimum codegree condition for the existence of a perfect tiling of a $3$ -uniform hypergraph $H$ with copies of the generalised triangle $T$ , which is…

math.CO2024

Improved bounds for proper rainbow saturation

Andrew Lane, Natasha Morrison

Given a graph $H$ , we say that a graph $G$ is properly rainbow $H$ -saturated if: (1) There is a proper edge colouring of $G$ containing no rainbow copy of $H$ ; (2) For every $e \no…

math.CO2024

Proper rainbow saturation for trees

Andrew Lane, Natasha Morrison

Given a graph $H$ , we say that a graph $G$ is properly rainbow $H$ -saturated if: (1) There is a proper edge colouring of $G$ containing no rainbow copy of $H$ ; (2) For every $e \no…