Songling Shan

activity

20142024

most citedNonempty intersection of longest paths in

2 K_{2}

-free graphs

5 citations · 8 across the 11 of their papers we have counts for

collaborators

12 papers

math.CO2025

Hamilton cycles in tough $(2 P_{2} \cup P_{1})$ -free graphs

Songling Shan, Arthur Tanyel

In 1973, Chvátal conjectured that there exists a constant $t_{0}$ such that every $t_{0}$ -tough graph on at least three vertices is Hamiltonian. While this conjecture is still open, wo…

math.CO2024

A reduction of the "cycles plus $K_{4}$ 's" problem

Aseem Dalal, Jessica McDonald, Songling Shan

Let $H$ be a 2-regular graph and let $G$ be obtained from $H$ by gluing in vertex-disjoint copies of $K_{4}$ . The "cycles plus $K_{4}$ 's" problem is to show that $G$ is 4-colourable; t…

math.CO2024

Spanning Euler Tours in Hypergraphs

Amin Bahmanian, Songling Shan

Motivated by generalizations of de Bruijn cycles to various combinatorial structures (Chung, Diaconis, and Graham), we study various Euler tours in set systems. Let $G$ b…

math.CO2023

Triangle-degree and triangle-distinct graphs

Zhanar Berikkyzy, Beth Bjorkman, Heather Smith Blake +5

Let $G$ be a simple graph and $v$ be a vertex of $G$ . The triangle-degree of $v$ in $G$ is the number of triangles that contain $v$ . While every graph has at least two vertices wit…

math.CO2023

A note on Gupta's co-density conjecture

Guantao Chen, Songling Shan

Let $G$ be a multigraph. A subset $F$ of $E (G)$ is an edge cover of $G$ if every vertex of $G$ is incident to an edge of $F$ . The cover index, $ξ (G)$ , is the largest number of edge…

math.CO2022

Overfullness of edge-critical graphs with small minimal core degree

Yan Cao, Guantao Chen, Guangming Jing +1

Let $G$ be a simple graph. Denote by $n$ , $Δ (G)$ and $χ^{'} (G)$ be the order, the maximum degree and the chromatic index of $G$ , respectively. We call $G$ \emph{overfull} if $|E(G)|/…

Hamilton cycles in tough (2P2​∪P1​)-free graphs