3 papers
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…
math.CO2024
Note on a conjecture of Talagrand: expectation thresholds vs. fractional expectation thresholds
Quentin Dubroff, Jeff Kahn, Jinyoung Park
We show that a restricted version of a conjecture of M. Talagrand on the relation between "expectation thresholds" and "fractional expectation thresholds" follows easily from a str…