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math.CO2022
On Meyniel extremal families of graphs
Anthony Bonato, Ryan Cushman, Trent G. Marbach
We provide new constructions of Meyniel extremal graphs, which are families of graphs with the conjectured largest asymptotic cop number. Using spanning subgraphs, we prove that th…
math.CO2020
Closing the Random Graph Gap in Tuza's Conjecture Through the Online Triangle Packing Process
Patrick Bennett, Ryan Cushman, Andrzej Dudek
A long-standing conjecture of Zsolt Tuza asserts that the triangle covering number is at most twice the triangle packing number , where the triangle packing number $ν(…
math.CO2020
On the number of alternating paths in random graphs
Patrick Bennett, Ryan Cushman, Andrzej Dudek
In the noisy channel model from coding theory, we wish to detect errors introduced during transmission by optimizing various parameters of the code. Bennett, Dudek, and LaForge fra…