4 citations · 11 across the 12 of their papers we have counts for
13 papers · 1 filter
The Explorer-Director Game on Graphs
Pat Devlin, Erin Meger, Abigail Raz +1
The Explorer-Director game, first introduced by Nedev and Muthukrishnan, can be described as a game where two players -- Explorer and Director -- determine the movement of a token…
Perfect matchings and derangements on graphs
Matija Bucic, Pat Devlin, Mo Hendon +2
We show that each perfect matching in a bipartite graph intersects at least half of the perfect matchings in . This result has equivalent formulations in terms of the perman…
Connected-Intersecting Families of Graphs
Aaron Berger, Ross Berkowitz, Pat Devlin +4
For a graph property and a common vertex set , a family of graphs on is \emph{-intersecting} iff satisfies $\math…
Expected Chromatic Number of Random Subgraphs
Ross Berkowitz, Pat Devlin, Catherine Lee +2
Given a graph and , let denote the random subgraph of obtained by keeping each edge independently with probability . Alon, Krivelevich, and Sudokov pr…
Hamiltonian Berge cycles in random hypergraphs
Deepak Bal, Ross Berkowitz, Pat Devlin +1
In this note, we study the emergence of Hamiltonian Berge cycles in random -uniform hypergraphs. For , we prove an optimal stopping-time result that if edges are sequen…
Two-vertex generators of Jacobians of graphs
David Brandfonbrener, Pat Devlin, Netanel Friedenberg +4
We give necessary and sufficient conditions under which the Jacobian of a graph is generated by a divisor that is the difference of two vertices. This answers a question posed by B…