Zhen He

activity

20232026

collaborators

10 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-colored graph $(G, C)$ is $F$ -rainbow saturated if it contains no rainbow copy of $F$ , but adding any nonedge in any prescribed color creates one. The rainbow satur…

math.CO2024

Partite saturation number of cycles

Yiduo Xu, Zhen He, Mei Lu

A graph $H$ 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 copy of $…

math.CO2024

The saturation number for unions of four cliques

Ruo-Xuan Li, Rong-Xia Hao, Zhen He +1

A graph $G$ is $H$ -saturated if $H$ is not a subgraph of $G$ but $H$ is a subgraph of $G + e$ for any edge $e$ in $G$ . The saturation number $s a t (n, H)$ for a graph $H$ i…

math.CO2024

Saturation Numbers for Linear Forests $P_{7} + t P_{2}$

Yu Zhang, Rong-Xia Hao, Zhen He +1

Let $H$ be a fixed graph, a graph G is $H$ -saturated if it has no copy of $H$ in $G$ , but the addition of any edge in $E (G)$ to $G$ results in an $H$ -subgraph. The satura…

math.CO2024

Minimum saturated graphs for unions of cliques

Wen-Han Zhu, Rong-Xia Hao, Zhen He

Let $H$ be a fixed graph. A graph $G$ is called {\it $H$ -saturated} if $H$ is not a subgraph of $G$ but the addition of any missing edge to $G$ results in an $H$ -subgraph. The {\it…

math.CO2023

Planar graphs without $5^{-}$ -cycles at distance less than $3$ are $(I, F)$ -colorable

Zhen He, Tao Wang, Xiaojing Yang

A graph is $(I, F)$ -colorable if its vertex set can be partitioned into two subsets, one of which is an independent set, and the other induces a forest. In this…

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

Partite saturation number of cycles

The saturation number for unions of four cliques

Saturation Numbers for Linear Forests P7​+tP2​

Minimum saturated graphs for unions of cliques

Planar graphs without 5−-cycles at distance less than 3 are (I,F)-colorable

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

Saturation Numbers for Linear Forests $P_{7} + t P_{2}$

Planar graphs without $5^{-}$ -cycles at distance less than $3$ are $(I, F)$ -colorable