Hongxia Ma

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math.CO2025

On the enumeration of connected sets in finite cylindrical lattice graphs

Hongxia Ma, Xian'an Jin, Meiqiao Zhang

A connected set in a graph is a non-empty set of vertices that induces a connected subgraph. In an infinite lattice, a connected set is often referred to as a lattice animal, whose…

math.CO2025

A sharp upper bound for the number of connected sets in any grid graph

Hongxia Ma, Xian'an Jin, Weiling Yang +1

A connected set in a graph is a subset of vertices whose induced subgraph is connected. Although counting the number of connected sets in a graph is generally a \#P-complete proble…

math.CO2024

Tight Toughness and Isolated Toughness for ${K_{2}, C_{n}}$ -factor critical avoidable graph

Xiaxia Guan, Hongxia Ma, Maoqun Wang

A spannning subgraph $F$ of $G$ is a ${K_{2}, C_{n}}$ -factor if each component of $F$ is either $K_{2}$ or $C_{n}$ . A graph $G$ is called a $({K_{2}, C_{n}}, n)$ -factor critical avoidable…

On the enumeration of connected sets in finite cylindrical lattice graphs

A sharp upper bound for the number of connected sets in any grid graph

Tight Toughness and Isolated Toughness for {K2​,Cn​}-factor critical avoidable graph

Tight Toughness and Isolated Toughness for ${K_{2}, C_{n}}$ -factor critical avoidable graph