Xichao Shu

collaborators

5 papers

math.CO2026

Tight Hamilton Cycles in Linearly Quasirandom 3-Graphs

Xichao Shu

We study tight Hamilton cycles in linearly quasirandom $3$ -graphs. An $n$ -vertex $3$ -graph $H$ is $(p, μ)$ -dense if $e_{H} (X, Y, Z) \geq p ∣ X ∣∣ Y ∣∣ Z ∣ - μ n^{3}$ for all $X, Y, Z \subseteq V (H)$ . Ar…

math.CO2026

Abundance of Unique Subhypergraphs

Xichao Shu, Zhuo Wu, Yisai Xue

Given $k$ -uniform hypergraphs $G$ and $H$ , we say that $G$ is a unique subhypergraph of $H$ if $H$ contains exactly one subhypergraph isomorphic to $G$ . For an $n$ -vertex $k$ -graph…

math.CO2026

A dichotomy for hypergraph Zarankiewicz problems on axis-parallel boxes

Ting-Wei Chao, Zichao Dong, Hong Liu +2

We study the Zarankiewicz problem for $r$ -partite, $r$ -uniform intersection hypergraphs arising from $r$ families of axis-parallel boxes in $R^{d}$ with prescribed direction…

math.CO2026

Fundamental cycles in grid graphs

Bartłomiej Kielak, Daniel Král', Ander Lamaison +1

We show that the average length of a fundamental cycle with respect to any fixed spanning tree of the $n \times n$ square grid is at least $Ω (lo g n)$ ; the bound is asymptotically t…

math.CO2024

Four-coloring Eulerian triangulations of the torus

Marcin Brianski, Daniel Kral, Ander Lamaison +1

Hutchinson, Richter and Seymour [J. Combin. Theory Ser. B 84 (2002), 225-239] showed that every Eulerian triangulation of an orientable surface that has a sufficiently high represe…