Hong‐Jian Lai

collaborators

3 papers

math.CO2023

Square Coloring of Planar Graphs with Maximum Degree at Most Five

Jiani Zou, Miaomiao Han, Hong-Jian Lai

The \textit{square} of a graph $G$ , denoted by $G^{2}$ , is obtained from $G$ by adding an edge to connect every pair of vertices with a common neighbor in $G$ . In this paper we prove…

math.CO2023

No mixed graph with the nullity $η (G) = ∣ V (G) ∣ - 2 m (G) + 2 c (G) - 1$

Shengjie He, Rong-Xia Hao, Hong-Jian Lai +1

A mixed graph $G$ is obtained from a simple undirected graph $G$ , the underlying graph of $G$ , by orienting some edges of $G$ . Let $c (G) = ∣ E (G) ∣ - ∣ V (G) ∣ + ω (G)$ …

math.CO2016

Nowhere-zero $3$ -flow and $Z_{3}$ -connectedness in Graphs with Four Edge-disjoint Spanning Trees

Miaomiao Han, Hong-Jian Lai, Jiaao Li

Given a zero-sum function $β : V (G) \to Z_{3}$ with $\sum_{v \in V (G)} β (v) = 0$ , an orientation $D$ of $G$ with $d_{D}^{+} (v) - d_{D}^{-} (v) = β (v)$ in $Z_{3}$ for every ver…

Square Coloring of Planar Graphs with Maximum Degree at Most Five

No mixed graph with the nullity η(G)=∣V(G)∣−2m(G)+2c(G)−1

Nowhere-zero 3-flow and Z3​-connectedness in Graphs with Four Edge-disjoint Spanning Trees

No mixed graph with the nullity $η (G) = ∣ V (G) ∣ - 2 m (G) + 2 c (G) - 1$

Nowhere-zero $3$ -flow and $Z_{3}$ -connectedness in Graphs with Four Edge-disjoint Spanning Trees