In a recent paper, Park and Pham famously proved Kahn-Kalai conjecture. In this note, we simplify their proof, using an induction to replace the original analysis. This reduces the proof to one page and from the argument it is also easy to read that one can set the constant $K$ in the conjecture to $\approx 3.998$, which could be the best value under the current method. Our argument also applies to the $\epsilon$-version of the Park-Pham result, studied by Bell.
@article{10_37236_12266,
author = {Phuc Tran and Van Vu},
title = {A short proof of {Kahn-Kalai} conjecture},
journal = {The electronic journal of combinatorics},
year = {2024},
volume = {31},
number = {3},
doi = {10.37236/12266},
zbl = {1548.05301},
url = {http://geodesic.mathdoc.fr/articles/10.37236/12266/}
}
TY - JOUR
AU - Phuc Tran
AU - Van Vu
TI - A short proof of Kahn-Kalai conjecture
JO - The electronic journal of combinatorics
PY - 2024
VL - 31
IS - 3
UR - http://geodesic.mathdoc.fr/articles/10.37236/12266/
DO - 10.37236/12266
ID - 10_37236_12266
ER -
%0 Journal Article
%A Phuc Tran
%A Van Vu
%T A short proof of Kahn-Kalai conjecture
%J The electronic journal of combinatorics
%D 2024
%V 31
%N 3
%U http://geodesic.mathdoc.fr/articles/10.37236/12266/
%R 10.37236/12266
%F 10_37236_12266
