Xin Zhang

collaborators

11 papers

math.CO2026

An improved upper bound for the planar TurÃ¡n 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 SchÃ¼lke, 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

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

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

Exact rainbow numbers of cycle-related graphs in multi-hubbed wheels

Mengyao Dai, Xin Zhang

The rainbow number $rb (G, H)$ is the minimum number of colors $k$ for which any edge-coloring of $G$ with at least $k$ colors guarantees a rainbow subgraph isomorphic to $H$ .…

math.CO2025

Fast algorithm for $S$ -packing coloring of Halin graphs

Xin Zhang, Dezhi Zou

Motivated by frequency assignment problems in wireless broadcast networks, Goddard, Hedetniemi, Hedetniemi, Harris, and Rall introduced the notion of $S$ -packing coloring in 2008.…

An improved upper bound for the planar TurÃ¡n number of C8​

Bootstrap percolation of extension hypergraphs

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

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

Exact rainbow numbers of cycle-related graphs in multi-hubbed wheels

Fast algorithm for S-packing coloring of Halin graphs

An improved upper bound for the planar TurÃ¡n number of $C_{8}$

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

Fast algorithm for $S$ -packing coloring of Halin graphs