83 citations · 346 across the 78 of their papers we have counts for
5 papers · 1 filter
The game of Overprescribed Cops and Robbers played on graphs
Anthony Bonato, Xavier Pérez-Giménez, Paweł Prałat +1
We consider the effect on the length of the game of Cops and Robbers when more cops are added to the game play. In Overprescribed Cops and Robbers, as more cops are added, the capt…
The Total Acquisition Number of Random Geometric Graphs
Ewa Infeld, Dieter Mitsche, Pawel Pralat
Let be a graph in which each vertex initially has weight 1. In each step, the weight from a vertex to a neighbouring vertex can be moved, provided that the weight on $v…
Perfect matchings and Hamiltonian cycles in the preferential attachment model
Alan Frieze, Xavier Pérez-Giménez, Paweł Prałat +1
In this paper, we study the existence of perfect matchings and Hamiltonian cycles in the preferential attachment model. In this model, vertices are added to the graph one by one, a…
Size-Ramsey numbers of cycles versus a path
Andrzej Dudek, Farideh Khoeini, Paweł Prałat
The size-Ramsey number of a family of graphs and a graph is the smallest integer such that there exists a graph on edges with…
Rainbow perfect matchings and Hamilton cycles in the random geometric graph
Deepak Bal, Patrick Bennett, Xavier Pérez-Giménez +1
Given a graph on vertices and an assignment of colours to the edges, a rainbow Hamilton cycle is a cycle of length visiting each vertex once and with pairwise different col…