Weichan Liu

activity

20172026

most citedOdd coloring of 2-boundary planar graphs and beyond

2 citations · 3 across the 14 of their papers we have counts for

collaborators

14 papers

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

Covering graphs by isometric trees

Paul Bastide, Julien Duron, Jędrzej Hodor +2

A connected subgraph of a graph is isometric if it preserves distances. Recently, graphs admitting a vertex or edge covering by a small number of isometric paths have been studied.…

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…

math.CO2025

Equitable coloring of graphs beyond planarity

Weichan Liu

An equitable coloring of a graph is a proper coloring where the sizes of any two different color classes do not differ by more than one. A graph is IC-planar if it can be drawn in…

math.CO2025

Independent transversal blow-up of graphs

Tianjiao Dai, Weichan Liu, Xin Zhang

In an $r$ -partite graph, an independent transversal of size $s$ (ITS) consists of $s$ vertices from each part forming an independent set. Motivated by a question from Bollobás, Erd…

math.CO2025

Infinitely many accumulation points of codegree Turán densities

Heng Li, Weichan Liu, Bjarne Schülke +1

The codegree Turán density $γ (F)$ of a $k$ -graph $F$ is the smallest $γ \in [0, 1)$ such that every $k$ -graph $H$ with $δ_{k - 1} (H) \geq (γ + o (1)) ∣ V (H) ∣$ contains a copy of $F$ .…

math.CO2024★ 1 cited

Equitable coloring of sparse graphs

Weichan Liu, Xin Zhang

An equitable coloring of a graph is a proper coloring where the sizes of any two distinct color classes differ by at most one. The celebrated Chen-Lih-Wu Conjecture (CLWC for short…

math.CO2024

Cooperative colorings of hypergraphs

Xuqing Bai, Bi Li, Weichan Liu +1

Given a class $H$ of $m$ hypergraphs $H_{1}, H_{2}, \dots, H_{m}$ with the same vertex set $V$ , a cooperative coloring of them is a partition ${I_{1}, I_{2}, \dots, I_{m}}$ …

math.CO2022★ 2 cited

Odd coloring of 2-boundary planar graphs and beyond

Weichan Liu, Mengke Qi, Xin Zhang

In this paper, we introduce the notion of 2-boundary planar graphs. A graph is 2-boundary planar if it has an embedding in the plane so that all vertices lie on the boundary of at…

math.CO2022

Hypergraph incidence coloring

Weichan Liu, Guiying Yan

An incidence of a hypergraph $H = (X, S)$ is a pair $(x, s)$ with $x \in X$ , $s \in S$ and $x \in s$ . Two incidences $(x, s)$ and $(x^{'}, s^{'})$ are adjacent if (i) $x = x^{'}$ , or (ii) $\…

math.CO2017

A note on the vertex arboricity of signed graphs

Weichan Liu, Chen Gong, Lifang Wu +1

A signed tree-coloring of a signed graph $(G, σ)$ is a vertex coloring $c$ so that $G^{c} (i, \pm)$ is a forest for every $i \in c (u)$ and $u \in V (G)$ , where $G^{c} (i, \pm)$ is the subg…

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

Covering graphs by isometric trees

Perfect tilings with the generalised triangle in k-graphs

Local rainbow colorings of hypergraphs

Equitable coloring of graphs beyond planarity

Independent transversal blow-up of graphs

Infinitely many accumulation points of codegree Turán densities

Equitable coloring of sparse graphs

Cooperative colorings of hypergraphs

Odd coloring of 2-boundary planar graphs and beyond

Hypergraph incidence coloring

A note on the vertex arboricity of signed graphs

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

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