Xiaopan Lian

activity

20202026

most citedOn a variant of dichromatic number for digraphs with prescribed sets of arcs

1 citations · 2 across the 9 of their papers we have counts for

collaborators

11 papers

math.CO2026

An improved upper bound for oriented diameter of graphs with diameter $4$

Yaokun Feng, Hui Lei, Xiaopan Lian +1

Let $f (d)$ denote the smallest integer such that every bridgeless graph of diameter $d$ admits a strong orientation with diameter at most $f (d)$ . It is known that $f (2) = 6$ and $f(3…

math.CO2025

A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs

Jasmin Katz, Xiaopan Lian, Alexandru Malekshahian +1

Let $G$ be a graph and $Γ$ a finite abelian group. The zero-sum Ramsey number of $G$ over $Γ$ , denoted by $R (G, Γ)$ , is the smallest positive integer $t$ (if it exists) such that a…

math.CO2023

Tight upper bound on the clique size in the square of 2-degenerate graphs

Seog-Jin Kim, Xiaopan Lian

The {\em square} of a graph $G$ , denoted $G^{2}$ , has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$ . In general,…

math.CO2023★ 1 cited

On a variant of dichromatic number for digraphs with prescribed sets of arcs

O-joung Kwon, Xiaopan Lian

In this paper, we consider a variant of dichromatic number on digraphs with prescribed sets of arcs. Let $D$ be a digraph and let $Z_{1}, Z_{2}$ be two sets of arcs in $D$ . For a subdi…

math.CO2023

The square of every subcubic planar graph of girth at least 6 is 7-choosable

Seog-Jin Kim, Xiaopan Lian

The square of a graph $G$ , denoted $G^{2}$ , has the same vertex set as $G$ and has an edge between two vertices if the distance between them in $G$ is at most $2$ . Thomassen (2018) a…

math.CO2023

Group vertex-arboricity of group-labelled graphs

O-joung Kwon, Xiaopan Lian

We introduce the vertex-arboricity of group-labelled graphs. For an abelian group $Γ$ , a $Γ$ -labelled graph is a graph whose edges are labelled by elements of $Γ$ . For an abelian g…

math.CO2022

Some Mader-perfect graph classes

Hui Lei, Siyan Li, Xiaopan Lian +1

The dichromatic number of $D$ , denoted by $χ (D)$ , is the smallest integer $k$ such that $D$ admits an acyclic $k$ -coloring. We use $ma d e r_{χ} (F)$ to d…

math.CO2022

Weak-odd chromatic index of special digraph classes

Ruijuan Gu, Hui Lei, Xiaopan Lian +1

Give a digraph $D = (V (D), A (D))$ , let $\partial_{D}^{+} (v) = {v w ∣ w \in N_{D}^{+} (v)}$ and $\partial_{D}^{-} (v) = {uv ∣ u \in N_{D}^{-} (v)}$ be semi-cuts of $v$ . A mapping $φ : A (D) \to [k]$ is call…

math.CO2021

On critical graphs for the chromatic edge-stability number

Hui Lei, Xiaopan Lian, Xianhao Meng +2

The {\em chromatic edge-stability number} $e s_{χ} (G)$ of a graph $G$ is the minimum number of edges whose removal results in a spanning subgraph with the chromatic number smaller tha…

math.CO2021

A characterization of 4- $χ_{S}$ -vertex-critical graphs for packing sequences with $s_{1} = 1$ and $s_{2} \geq 3$

Sandi Klavžar, Hui Lei, Xiaopan Lian +1

If $S = (s_{1}, s_{2}, \dots)$ is a non-decreasing sequence of positive integers, then the $S$ -packing $k$ -coloring of a graph $G$ is a mapping $c : V (G) \to [k]$ such that if $c(u)=…

math.CO2020★ 1 cited

Some extremal results on the chromatic-stability index

Shenwei Huang, Sandi Klavžar, Hui Lei +2

The $χ$ -stability index $es_{χ} (G)$ of a graph $G$ is the minimum number of its edges whose removal results in a graph with the chromatic number smaller than that of $G$ . In th…

An improved upper bound for oriented diameter of graphs with diameter 4

A linear upper bound for zero-sum Ramsey numbers of bounded degree graphs

Tight upper bound on the clique size in the square of 2-degenerate graphs

On a variant of dichromatic number for digraphs with prescribed sets of arcs

The square of every subcubic planar graph of girth at least 6 is 7-choosable

Group vertex-arboricity of group-labelled graphs

Some Mader-perfect graph classes

Weak-odd chromatic index of special digraph classes

On critical graphs for the chromatic edge-stability number

A characterization of 4-χS​-vertex-critical graphs for packing sequences with s1​=1 and s2​≥3

Some extremal results on the chromatic-stability index

An improved upper bound for oriented diameter of graphs with diameter $4$

A characterization of 4- $χ_{S}$ -vertex-critical graphs for packing sequences with $s_{1} = 1$ and $s_{2} \geq 3$