Weichan Liu

activity

20172026

collaborators

Showing math.COShow all

13 papers · 1 filter

math.CO2026

An improved upper bound for the planar Turán number of $C_{8}$

Xuqing Bai, Weichan Liu, Xiangxiang Nie +1

We prove that every $n$ -vertex simple planar graph with no copy of $C_{8}$ has at most \[ \frac{69}{25}(n-2) \] edges, for every $n \geq 8$ . This improves the best known bound \[ \frac…

math.CO2026

Bootstrap percolation of extension hypergraphs

Weichan Liu, Bjarne Schülke, Xin Zhang

For $k$ -graphs $F$ and $H_{0}$ the $F$ -bootstrap percolation process (or $F$ -process) starting with $H_{0}$ is a sequence $(H_{i})_{i \geq 0}$ of $k$ -graphs such that $H_{i + 1}$ is obtained…

math.CO2026

Upper bounds on the running time of bootstrap percolation

Weichan Liu, Xiangxiang Nie, Simón Piga +1

For $k$ -graphs $F$ and $H_{0}$ the $F$ -bootstrap percolation process (or $F$ -process) starting with $H_{0}$ is a sequence $(H_{i})_{i \geq 0}$ of $k$ -graphs such that $H_{i + 1}$ is obtained…

math.CO2025

Counterexamples to statements on isometric graph coverings

Paul Bastide, Julien Duron, Jędrzej Hodor +2

A connected subgraph of a graph is isometric if it preserves distances. In this short note, we provide counterexamples to several variants of the following general question: When a…

math.CO2025

Perfect tilings with the generalised triangle in $k$ -graphs

Weichan Liu, Xiangxiang Nie, Donglei Yang +1

Denote by $T_{k}$ the generalised triangle, a $k$ -uniform hypergraph on vertex set ${1, 2, \dots, 2 k - 1}$ with three edges ${1, \dots, k - 1, k}$ , ${1, \dots, k - 1, k + 1}$ and $\{k,k+1,\dots,…

math.CO2025

Local rainbow colorings of hypergraphs

Zhenyu Li, Weichan Liu, Guowei Sun +2

In this paper, we generalize the concepts related to rainbow coloring to hypergraphs. Specifically, an $(n, r, H)$ -local coloring is defined as a collection of $n$ edge-colorings, $f…

An improved upper bound for the planar Turán number of C8​

Bootstrap percolation of extension hypergraphs

Upper bounds on the running time of bootstrap percolation

Counterexamples to statements on isometric graph coverings

Perfect tilings with the generalised triangle in k-graphs

Local rainbow colorings of hypergraphs

An improved upper bound for the planar Turán number of $C_{8}$

Perfect tilings with the generalised triangle in $k$ -graphs