Andrew Lane

collaborators

3 papers

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…

math.CO2024

Generalized Ramsey numbers via conflict-free hypergraph matchings

Andrew Lane, Natasha Morrison

Given graphs $G, H$ and an integer $q \geq 2$ , the generalized Ramsey number, denoted $r (G, H, q)$ , is the minimum number of colours needed to edge-colour $G$ such that every copy of…