Alexander Roberts

activity

20182020

collaborators

6 papers

math.CO2020

Isoperimetric stability in lattices

Ben Barber, Joshua Erde, Peter Keevash +1

We obtain isoperimetric stability theorems for general Cayley digraphs on $Z^{d}$ . For any fixed $B$ that generates $Z^{d}$ over $Z$ , we characterise the app…

math.CO2019

Shotgun reconstruction in the hypercube

Michał Przykucki, Alexander Roberts, Alex Scott

Mossel and Ross raised the question of when a random colouring of a graph can be reconstructed from local information, namely the colourings (with multiplicity) of balls of given r…

math.CO2019

Maximising the Number of Cycles in Graphs with Forbidden Subgraphs

Natasha Morrison, Alexander Roberts, Alex Scott

Fix $k \geq 2$ and let $H$ be a graph with $χ (H) = k + 1$ containing a critical edge. We show that for sufficiently large $n$ , the unique $n$ -vertex $H$ -free graph containing the maxi…

math.CO2018

Vertex-isoperimetric stability in the hypercube

Michał Przykucki, Alexander Roberts

Harper's Theorem states that, in a hypercube, among all sets of a given fixed size the Hamming balls have minimal closed neighbourhoods. In this paper we prove a stability-like res…

math.CO2018

Approximating the position of a hidden agent in a graph

Hannah Guggiari, Alexander Roberts, Alex Scott

A cat and mouse play a pursuit and evasion game on a connected graph $G$ with $n$ vertices. The mouse moves to vertices $m_{1}, m_{2}, \dots$ of $G$ where $m_{i}$ is in the closed neighbou…

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…