6 citations · 7 across the 4 of their papers we have counts for
6 papers
Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery
Benjamin Przybocki, John Mackey, Marijn J. H. Heule +1
Ramsey-good graphs are graphs that contain neither a clique of size nor an independent set of size . We study doubly saturated Ramsey-good graphs, defined as Ramsey-good gra…
Tighter Bounds on Directed Ramsey Number R(7)
David Neiman, John Mackey, Marijn Heule
Tournaments are orientations of the complete graph, and the directed Ramsey number is the minimum number of vertices a tournament must have to be guaranteed to contain a tra…
The Resolution of Keller's Conjecture
Joshua Brakensiek, Marijn Heule, John Mackey +1
We consider three graphs, , , and , related to Keller's conjecture in dimension 7. The conjecture is false for this dimension if and only if at least one…
On the number of 5-cycles in a tournament
Natasha Komarov, John Mackey
We find an exact formula for the number of directed 5-cycles in a tournament in terms of its edge score sequence. We use this formula to find both upper and lower bounds on the num…
Containment: A Variation of Cops and Robbers
Danny Crytser, Natasha Komarov, John Mackey
We consider "Containment": a variation of the graph pursuit game of Cops and Robber in which cops move from edge to adjacent edge, the robber moves from vertex to adjacent vertex (…
Graham's Number is Less Than 2^^^6
Mikhail Lavrov, Mitchell Lee, John Mackey
In [5] Graham and Rothschild consider a geometric Ramsey problem: finding the least n such that if all edges of the complete graph on the points {+1,-1}^n are 2-colored, there exis…