Zhen He

collaborators

5 papers

math.CO2026

A note on the saturation number for unions of three cliques

Hanlai Lin, Zhen He, Yiduo Xu

A graph $G$ is $F$ -saturated if $G$ contains no copy of $F$ but $G + e$ contains a copy of $F$ for every missing edge $e$ of $G$ . The saturation number $\sat(n,F)$ is the minimum num…

math.CO2026

All minimum $C_{4}$ -saturated multipartite graphs

Yiduo Xu, Zhen He, Mei Lu +1

A subgraph $H$ of $G$ is said to be $F$ -saturated relative to $G$ , if $H$ does not contain any copy of $F$ , but the addition of any edge $e$ in $E (G) \ E (H)$ would create a…

math.CO2026

Degree-restricted semi-saturation numbers of cliques and its applications

Zhen He, Mei Lu, Yanzhe Qiu +1

A graph $G$ is said to be $F$ -semi-saturated if the addition of any nonedge $e \neq \in E (G)$ would create a new copy of $F$ in $G + e$ . The semi-saturation number $ss a t (n, F)$ is the…

math.CO2025

The saturation number of wheels

Yanzhe Qiu, Zhen He, Mei Lu +1

A graph $G$ is said to be $F$ -free, if $G$ does not contain any copy of $F$ . $G$ is said to be $F$ -semi-saturated, if the addition of any nonedge $e \neq \in E (G)$ would create a n…

math.CO2025

The Rainbow Saturation Number of Cycles

Yiduo Xu, Zhen He, Mei Lu

An edge-coloring of a graph $H$ is a function $C : E (H) \to N$ . We say that $H$ is rainbow if all edges of $H$ have different colors. Given a graph $F$ , a…

A note on the saturation number for unions of three cliques

All minimum C4​-saturated multipartite graphs

Degree-restricted semi-saturation numbers of cliques and its applications

The saturation number of wheels

The Rainbow Saturation Number of Cycles

All minimum $C_{4}$ -saturated multipartite graphs