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math.CO2025
On Minimum Cost Rainbow Structures
Patrick Bennett, Quentin Dubroff, Alan Frieze +1
We discuss the expected minimum cost of rainbow spanning trees and Hamilton cycles in randomly edge colored random graphs.
math.CO2025
On the "second" Kahn--Kalai Conjecture: cliques, cycles, and trees
Quentin Dubroff, Jeff Kahn, Jinyoung Park
We prove a few simple cases of a random graph statement that would imply the "second" Kahn--Kalai Conjecture. Even these cases turn out to be reasonably challenging, and it is hope…
math.CO2025
On the "second" Kahn--Kalai Conjecture
Quentin Dubroff, Jeff Kahn, Jinyoung Park
We make progress on a conjecture of Kahn and Kalai, the original (stronger but less general) version of what became known as the ``Kahn-Kalai Conjecture" (KKC; now a theorem of Par…