2 citations · 4 across the 5 of their papers we have counts for
6 papers · 1 filter
Creating Subgraphs in Semi-Random Hypergraph Games
Natalie Behague, Pawel Pralat, Andrzej Rucinski
The semi-random hypergraph process is a natural generalisation of the semi-random graph process, which can be thought of as a one player game. For fixed , starting with an e…
The localization capture time of a graph
Natalie C. Behague, Anthony Bonato, Melissa A. Huggan +2
The localization game is a pursuit-evasion game analogous to Cops and Robbers, where the robber is invisible and the cops send distance probes in an attempt to identify the locatio…
Subgraph Games in the Semi-Random Graph Process and Its Generalization to Hypergraphs
Natalie C. Behague, Trent G. Marbach, Pawel Pralat +1
The semi-random graph process is a single-player game that begins with an empty graph on vertices. In each round, a vertex is presented to the player independently and unif…
Tight Bounds on the Probabilistic Zero Forcing on Hypercubes and Grids
Natalie C. Behague, Trent Marbach, Pawel Pralat
Zero forcing is a deterministic iterative graph colouring process in which vertices are coloured either blue or white, and in every round, any blue vertices that have a single whit…
Synchronizing Times for -sets in Automata
Natalie C. Behague, J. Robert Johnson
An automaton is synchronizing if there is a word that maps all states onto the same state. Černý's conjecture on the length of the shortest such word is probably the most famous op…
Semi-perfect 1-Factorizations of the Hypercube
Natalie C. Behague
A 1-factorization of a graph is called perfect if the union of any pair of 1-factors with is a Hamilton cycle. It is…