83 citations · 346 across the 78 of their papers we have counts for
9 papers · 1 filter
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…
Broadcasting on Paths and Cycles
Reaz Huq, Pawel Pralat
Consider the following broadcasting process run on a connected graph . Suppose that agents start on vertices selected from uniformly and independently at ran…
The Unit Acquisition Number of Binomial Random Graphs
Konstantinos Georgiou, Somnath Kundu, Pawel Pralat
Let be a graph in which each vertex initially has weight 1. In each step, the unit weight from a vertex to a neighbouring vertex can be moved, provided that the weight…
Hamilton Cycles in the Semi-random Graph Process
Pu Gao, Bogumil Kaminski, Calum MacRury +1
The semi-random graph process is a single player game in which the player is initially presented an empty graph on vertices. In each round, a vertex is presented to the pla…
Analyzing, Exploring, and Visualizing Complex Networks via Hypergraphs using SimpleHypergraphs.jl
Alessia Antelmi, Gennaro Cordasco, Bogumił Kamiński +4
Real-world complex networks are usually being modeled as graphs. The concept of graphs assumes that the relations within the network are binary (for instance, between pairs of node…
On Broadcasting Time in the Model of Travelling Agents
Reaz Huq, Bogumil Kaminski, Atefeh Mashatan +2
Consider the following broadcasting process run on a connected graph . Suppose that agents start on vertices selected from uniformly and independently at ran…
Probabilistically Faulty Searching on a Half-Line
Anthony Bonato, Konstantinos Georgiou, Calum MacRury +1
We study -Faulty Search, a variant of the classic cow-path optimization problem, where a unit speed robot searches the half-line (or -ray) for a hidden item. The searcher is…
On the existence of Hamilton cycles with a periodic pattern in a random digraph
Alan Frieze, Xavier Perez-Gimenez, Pawel Pralat
We consider Hamilton cycles in the random digraph where the orientation of edges follows a pattern other than the trivial orientation in which the edges are oriented in t…
Artificial Benchmark for Community Detection (ABCD): Fast Random Graph Model with Community Structure
Bogumił Kamiński, Paweł Prałat, François Théberge
Most of the current complex networks that are of interest to practitioners possess a certain community structure that plays an important role in understanding the properties of the…