Author

Shuo Wei

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Preprint Aug 2026

An Exact Dominant Degree Condition for Transitive Tournament Factors in Digraphs

Let $r\ge2$, let $T_r$ denote the transitive tournament on $r$ vertices, and write $d_G^*(v):=\max\{d_G^+(v),d_G^-(v)\}$. We prove that if $r\mid n$ and an $n$-vertex digraph $G$ satisfies $d_G^*(x)+d_G^*(y)\ge 2(1-1/r)n-1$ for every $x\ne y \in V(G)$ with $xy \notin E(G)$, then $G$ has a $T_r$-factor, and the bound is...

Yu-jeong Chang, Shuo Wei, Jin Yan · 2 citations · ⚡1

Preprint Jul 2026

The exact total degree threshold for the square of a Hamilton cycle in digraphs

The P\'{o}sa-Seymour conjecture establishes the minimum degree threshold required to guarantee the presence of the $k$th power of a Hamilton cycle in a graph. Following numerous partial results, Koml\'{o}s, S\'{a}rk\"{o}zy, and Szemer\'{e}di confirmed the conjecture holds for all sufficiently large graphs. Treglown lat...

Zhilan Wang, Shuo Wei, Jin Yan · 0 citations