7 papers
Linear arboricity of robust expanders
Yuping Gao, Songling Shan
In 1980, Akiyama, Exoo, and Harary conjectured that any graph can be decomposed into at most linear forests. We confirm the conjecture for robust expa…
A sufficient condition for a hypergraph to have a Berge--factor
Yuping Gao, Songling Shan, Gexin Yu
For any graph (hypergraph) with vertex set and edge set , we define its incidence bipartite graph as the bipartite graph with bipartition , wher…
Vertex-distinguishing and sum-distinguishing edge coloring of regular graphs
Yuping Gao, Songling Shan, Guanghui Wang
Given an integer , an edge--coloring of a graph is an assignment of colors to the edges of such that no two adjacent edges receive the same color…
Towards the Overfull Conjecture
Songling Shan
Let be a simple graph with maximum degree denoted as . An overfull subgraph of is a subgraph satisfying the condition $|E(H)| > Î(G)\lfloor \frac{1}{2}|V(H)| \r…
Total coloring graphs with large maximum degree
Aseem Dalal, Jessica McDonald, Songling Shan
We prove that for any graph , the total chromatic number of is at most . This saves one color in comparison with a re…
A construction of a -tough plane triangulation with no 2-factor
Songling Shan
In 1956, Tutte proved the celebrated theorem that every 4-connected planar graph is hamiltonian. This result implies that every more than -tough planar graph on at lea…