Songling Shan

activity

20242026

collaborators

11 papers

math.CO2026

Vertex-distinguishing chromatic index of digraphs

Yuping Gao, Zijun Qin, Songling Shan

Let $D$ be a digraph. In this note, an \emph{arc coloring} of $D$ is an assignment of colors to the arcs of $D$ such that no two arcs with a common tail receive the same color and…

math.CO2026

Towards the Overfull Conjecture II

Guantao Chen, Jessica McDonald, Songling Shan

Let $G$ be a simple graph with maximum degree $I^ (G)$ . A subgraph $H \subseteq G$ is $I^ (G)$ -overfull if $∣ E (H) ∣ > I^ (G) ⌊ ∣ V (H) ∣/2 ⌋$ . In any edge coloring of $G…

math.CO2026

Exploring the world of edge-chromatic 3-critical graphs

Le Chen, Songling Shan

A graph $G$ with maximum degree $I^$ is $I^$ -critical if it is connected, satisfies $I ¨ ^{'} (G) = I^ + 1$ , and the deletion of any edge reduces its chromatic index to $I^$ . A $I^$ -critical…

math.CO2026

Equitable tree colouring of graphs

Yuping Gao, Allan Lo, Songling Shan

Let $k \in N$ and let $G$ be a simple graph with maximum degree $I^$ . A $k$ -colouring $I ¨ $ of $G$ is an assignment of colours from ${1, 2, \dots, k}$ to the vertices of $G…

math.CO2025

Vertex-distinguishing edge coloring of graphs

Yuping Gao, Songling Shan, Guanghui Wang +1

Let $k \geq 1$ be an integer and let $G$ be a nonempty simple graph. An \emph{edge- $k$ -coloring} $I ¨ $ of $G$ is an assignment of colors from ${1, \dots, k}$ to the edges of $G$ suc…

math.CO2025

Degree sequences realizing labelled perfect matchings

Joseph Briggs, Jessica McDonald, Songling Shan

Let $n \in N$ and $d_{1} \geq d_{2} \geq d_{n} \geq 1$ be integers. There is characterization of when $(d_{1}, d_{1}, \dots, d_{n})$ is the degree sequence of a graph containing a perf…