19 citations · 46 across the 26 of their papers we have counts for
5 papers · 1 filter
Square of a Hamilton cycle in a random graph
Patrick Bennett, Andrzej Dudek, Alan Frieze
We show that the threshold for the random graph to contain the square of a Hamilton cycle is . This improves the previous results of Kühn and Osthus…
Square of Hamilton cycle in a random graph
Andrzej Dudek, Alan Frieze
We show that is a sharp threshold for the random graph to contain the square of a Hamilton cycle. This improves the previous results of Kühn and Os…
On the number of alternating paths in bipartite complete graphs
Patrick Bennett, Andrzej Dudek, Elliot Laforge
Let be a code such that any two words of have Hamming distance at least . It is not difficult to see that determining a code with the maximum number…
The Matching Process and Independent Process in Random Regular Graphs and Hypergraphs
Deepak Bal, Patrick Bennett
In this note, we analyze two random greedy processes on sparse random graphs and hypergraphs with a given degree sequence. First we analyze the matching process, which builds a set…
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…