5 papers · 1 filter
Equilibria in a Hypercube Spatial Voting Model
A. Nicholas Day, J. Robert Johnson
We give conditions for equilibria in the following Voronoi game on the discrete hypercube. Two players position themselves in and each receives payoff equal to the meas…
Asymmetry of 2-step Transit Probabilities in 2-Coloured Regular Graphs
Ron Gray, J. Robert Johnson
Suppose that the vertices of a regular graph are coloured red and blue with an equal number of each (we call this a balanced colouring). Since the graph is undirected, the number o…
Partial shuffles by lazy swaps
Barnabás Janzer, J. Robert Johnson, Imre Leader
What is the smallest number of random transpositions (meaning that we swap given pairs of elements with given probabilities) that we can make on an -point set to ensure that eac…
The -free process in the hypercube
J. Robert Johnson, Trevor Pinto
The generation of a random triangle-saturated graph via the triangle-free process has been studied extensively. In this short note our aim is to introduce an analogous process in t…
Transitive Avoidance Games
J. Robert Johnson, Imre Leader, Mark Walters
Positional games are a well-studied class of combinatorial game. In their usual form, two players take turns to play moves in a set (`the board'), and certain subsets are designate…