30 citations · 80 across the 21 of their papers we have counts for
6 papers · 1 filter
Sharpness in the k-nearest neighbours random geometric graph model
Victor Falgas-Ravry, Mark Walters
Let denote the random geometric graph obtained by placing points in a square box of area according to a Poisson process of intensity 1 and joining each point to its $…
Small components in k-nearest neighbour graphs
Mark Walters
Let denote the graph formed by placing points in a square of area according to a Poisson process of density 1 and joining each point to its nearest neighbours.…
Hamilton cycles in random geometric graphs
József Balogh, Béla Bollobás, Michael Krivelevich +2
We prove that, in the Gilbert model for a random geometric graph, almost every graph becomes Hamiltonian exactly when it first becomes 2-connected. This answers a question of Penro…
A critical constant for the k nearest neighbour model
Paul Balister, Bela Bollobas, Amites Sarkar +1
Let P be a Poisson process of intensity one in a square S_n of area n. For a fixed integer k, join every point of P to its k nearest neighbours, creating an undirected random geome…
Rigorous confidence intervals for critical probabilities
Oliver Riordan, Mark Walters
We use the method of Balister, Bollobas and Walters to give rigorous 99.9999% confidence intervals for the critical probabilities for site and bond percolation on the 11 Archimedea…
Continuum percolation with steps in an annulus
Paul Balister, Bela Bollobas, Mark Walters
Let A be the annulus in R^2 centered at the origin with inner and outer radii r(1-ε) and r, respectively. Place points {x_i} in R^2 according to a Poisson process with intensity 1…