Author

Zhenhua Lyu

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Preprint Aug 2026

The Exact End-Degree Threshold for Finite-Width Directed Hexagonal Grids

Grid theorems provide a fundamental link between the structure of ends and the existence of grid-like subgraphs in infinite graphs and digraphs. For every fixed width $n$, let $k(n)$ denote the least positive integer such that every digraph with an end of in-degree at least $k(n)$ contains a subdivision of the directed...

Dan Zhu, Zhenhua Lyu · 0 citations

Preprint Sep 2026

Polynomial Compressibility and Forbidden Oriented Forests

For a nonempty acyclic oriented graph $H$, let $p(H)$ be the order of a longest directed path and let $\tau(H)$ be the least positive integer $n$ such that $H$ admits a homomorphism to every tournament of order $n$. For all $p\ge3$ and $g\ge1$, we construct a connected acyclic oriented graph $H$ with underlying girth g...

Zhenhua Lyu · 0 citations

Preprint Aug 2026

The Prescribed-Vertex Semidegree Threshold for Directed $3q$-Cycles in Oriented Graphs

For every $q\ge2$, we prove that every oriented graph $G$ on $n\ge45q-8$ vertices whose minimum semidegree satisfies \[ \delta^0(G)\ge \left\lceil\frac n3\right\rceil \] contains a directed cycle of length $3q$ through every vertex. The semidegree bound is sharp. This closes the one-unit gap left by the prescribed-vert...

Zhenhua Lyu · 0 citations