Author

Tuan Tran

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Preprint Sep 2026

Fractional expectation thresholds and the"second"Kahn-Kalai conjecture

We show that the uniform probability measure on copies of a nonempty graph $H$ in $K_n$ is $Cq_H\log(2e(H))$-spread, where $q_H$ is its graphic expectation threshold. Consequently, the fractional expectation threshold of $H$ is at most $Cq_H\log(2e(H))$. We remove the logarithmic factor for trees and for graphs whose a...

Tuan Tran · 0 citations

Preprint Oct 2026

The threshold for fractional clique decompositions of random hypergraphs, via matrix scaling

Let $\delta^*_{k,r}$ be the fractional $K_r^{(k)}$-decomposition threshold in minimum codegree. For fixed $k\ge2$, $r\ge k+1$ and $\varepsilon>0$, we prove that every $n$-vertex $k$-uniform hypergraph $G$ with minimum codegree at least $(\delta^*_{k,r}+\varepsilon)n$ admits, with high probability, a fractional $K_r^{(k...

Tuan Tran · 0 citations

Preprint Aug 2026

Three trees suffice for a constant stretch in minor-free graphs

In this short note, we show that $H$-minor-free graphs have a tree cover with $3$ trees and constant stretch for any fixed graph $H$. The number of trees matches the recent lower bound by Chen, Tan, and Xu who showed that a toroidal grid requires at least $3$ trees for constant stretch. Our result is obtained by establ...

Hung Le, H. Pham, Cuong V. Than et al. · 0 citations