Xujun Liu

activity

20242026

collaborators

6 papers

math.CO2026

Between proper and square colorings of planar graphs with maximum degree at most four

Xujun Liu, Zihui Xu, Xin Zhang

An $i$ -independent set is a vertex set whose pairwise distance is at least $i + 1$ . A proper (square) $k$ -coloring of a graph $G$ is a partition of its vertex set into $k$ independen…

math.CO2026

Every connected subcubic graph except the Petersen graph is packing $(1, 1, 2, 2)$ -colorable

Xinmin Hou, Xujun Liu, Xiangyang Wang

For a non-decreasing sequence $S = (s_{1}, s_{2}, \dots, s_{k})$ of positive integers, a packing $S$ -coloring of a graph $G$ is a partition of $V (G)$ into $V_{1}, V_{2}, \dots, V_{k}$ such t…

math.CO2026

On $(1^{2}, 2^{2})$ -packing edge-coloring of sparse subcubic graphs

Xujun Liu, Jiacheng Yang, Xin Zhang

For positive integers $ℓ$ and $k$ , a $(1^{ℓ}, 2^{k})$ -packing edge-coloring of a graph $G$ is a partition of $E (G)$ into $ℓ$ matchings and $k$ induced matchings. A graph is $d…

math.CO2025

Between proper and square colorings of sparse graphs

Ilkyoo Choi, Xujun Liu

An $i$ -independent set is a set of vertices whose pairwise distance is at least $i + 1$ . A proper coloring (resp. a square coloring) of a graph is a partition of its vertices into in…

math.CO2025

Partition subcubic planar graphs into independent sets

Xujun Liu, Yan Wang

A packing $(1^{ℓ}, 2^{k})$ -coloring of a graph $G$ is a partition of $V (G)$ into $ℓ$ independent sets and $k$ $2$ -packings (whose pairwise vertex distance is at least $3$ ). The…

math.CO2024

Packing edge-colorings of subcubic outerplanar graphs

Sijin Li, Yifan Li, Xujun Liu

For a sequence $S = (s_{1}, s_{2}, \dots, s_{k})$ of non-decreasing positive integers, an $S$ -packing edge-coloring (S-coloring) of a graph $G$ is a partition of $E (G)$ into $E_1, E_2,…

Between proper and square colorings of planar graphs with maximum degree at most four

Every connected subcubic graph except the Petersen graph is packing (1,1,2,2)-colorable

On (12,22)-packing edge-coloring of sparse subcubic graphs

Between proper and square colorings of sparse graphs

Partition subcubic planar graphs into independent sets

Packing edge-colorings of subcubic outerplanar graphs

Every connected subcubic graph except the Petersen graph is packing $(1, 1, 2, 2)$ -colorable

On $(1^{2}, 2^{2})$ -packing edge-coloring of sparse subcubic graphs