Heping Zhang

activity

20242026

most citedMinimum forcing numbers of perfect matchings of circular and prismatic graphs

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

collaborators

6 papers

math.CO2026★ 1 cited

Minimum forcing numbers of perfect matchings of circular and prismatic graphs

Qiaoyun Shi, Heping Zhang

Let $G$ be a graph with a perfect matching. Denote by $f (G)$ the minimum size of a matching in $G$ that is uniquely extendable to a perfect matching in $G$ . Diwan (2019) used linea…

math.CO2026

Adjacent vertices of small degree in minimal matching covered graphs

Xiaoling He, Fuliang Lu, Heping Zhang

A connected graph $G$ with at least two vertices is matching covered if each of its edges lies in a perfect matching. A matching covered graph is minimal if the removal of any edge…

math.CO2026

On the $d$ -transversal number of cylindrical and toroidal grids

Hailun Wu, Heping Zhang

For a positive integer $d$ , a $d$ -transversal set of a graph $G$ is an edge subset $T \subseteq E (G)$ such that $∣ T \cap M ∣ \geq d$ for every maximum matching $M$ of $G$ . The $d$ -tran…

math.CO2025

On minimal k-factor-critical planar graphs

Qiuli Li, Fuliang Lu, Heping Zhang

A graph of order $n$ is said to be \emph{ $k$ -factor-critical} ( $0 \leq k < n$ ) if the removal of any $k$ vertices results in a graph with a perfect matching. A $k$ -factor-critical gr…

math.CO2025

The minimum degree of minimal 2-extendable claw-free graphs

Jing Guo, Fuliang Lu, Heping Zhang

A connected graph $G$ with a perfect matching is said to be $k$ -extendable for integers $k$ , $1 \leq k \leq \frac{∣ V ( G ) ∣}{2} - 1$ , if any matching in $G$ of size $k$ is contained in a…

math.CO2024

The minimum degree of minimal $k$ -factor-critical claw-free graphs*

Jing Guo, Qiuli Li, Fuliang Lu +1

A graph $G$ of order $n$ is said to be $k$ -factor-critical for integers $1 \leq k < n$ , if the removal of any $k$ vertices results in a graph with a perfect matching. A $k$ -factor-cr…