32 citations · 117 across the 58 of their papers we have counts for
12 papers · 1 filter
Lazy Cops and Robbers played on Graphs
Deepak Bal, Anthony Bonato, William B. Kinnersley +1
We consider a variant of the game of Cops and Robbers, called Lazy Cops and Robbers, where at most one cop can move in any round. We investigate the analogue of the cop number for…
Properties of metrics and infinite geometric graphs
Anthony Bonato, Jeannette Janssen
We consider isomorphism properties of infinite random geometric graphs defined over a variety of metrics. In previous work, it was shown that for with the $L_{\infty…
Distinguishing homomorphisms of infinite graphs
Anthony Bonato, Dejan Delic
We supply an upper bound on the distinguishing chromatic number of certain infinite graphs satisfying an adjacency property. Distinguishing proper -colourings are generalized to…
Models of on-line social networks
Anthony Bonato, Noor Hadi, Paul Horn +2
We present a deterministic model for on-line social networks (OSNs) based on transitivity and local knowledge in social interactions. In the Iterated Local Transitivity (ILT) model…
Meyniel's conjecture on the cop number: a survey
William Baird, Anthony Bonato
Meyniel's conjecture is one of the deepest open problems on the cop number of a graph. It states that for a connected graph of order While largely ig…
Vertex-pursuit in random directed acyclic graphs
Anthony Bonato, Dieter Mitsche, P. Pralat
We examine a dynamic model for the disruption of information flow in hierarchical social networks by considering the vertex-pursuit game Seepage played in directed acyclic graphs (…
The capture time of the hypercube
Anthony Bonato, William B. Kinnersley, P. Gordinowicz +1
In the game of Cops and Robbers, the capture time of a graph is the minimum number of moves needed by the cops to capture the robber, assuming optimal play. We prove that the captu…
The robber strikes back
Anthony Bonato, Stephen Finbow, Przemyslaw Gordinowicz +5
We consider the new game of Cops and Attacking Robbers, which is identical to the usual Cops and Robbers game except that if the robber moves to a vertex containing a single cop, t…
On the minimum order of k-cop-win graphs
William Baird, Andrew Beveridge, Anthony Bonato +4
We consider the minimum order graphs with a given cop number. We prove that the minimum order of a connected graph with cop number 3 is 10, and show that the Petersen graph is the…
A note on bounds for the cop number using tree decompositions
Anthony Bonato, N. E. Clarke, S. Finbow +2
In this short note, we supply a new upper bound on the cop number in terms of tree decompositions. Our results in some cases extend a previously derived bound on the cop number usi…
Independence densities of hypergraphs
Anthony Bonato, Jason Brown, Dieter Mitsche +1
We consider the number of independent sets in hypergraphs, which allows us to define the independence density of countable hypergraphs. Hypergraph independence densities include a…
Toppling numbers of complete and random graphs
A. Bonato, W. Kinnersley, P. Pralat
We study a two-person game played on graphs based on the widely studied chip-firing game. Players Max and Min alternately place chips on the vertices of a graph. When a vertex accu…