5 papers
An improved finite bound for oriented trees in tournaments
Jiangdong Ai, Xiaopan Lian
Sumner's universal tournament conjecture asserts that every tournament on vertices contains every oriented tree on vertices. Let be the least integer such tha…
The Alon-Tarsi Number of Squares of Subcubic Planar Graphs without Cycles of Lengths to
Seog-Jin Kim, Xiaopan Lian, Rong Luo
The Alon--Tarsi number of a graph , defined via the graph polynomial, is a strengthening of the list chromatic number . We study the Alon--Tarsi number of…
Edge-Number Bounds for the Inversion Diameter of Graphs
Jiawen Bo, Anqi Li, Xiaopan Lian +1
The inversion of a set of vertices in an oriented graph reverses every arc with both endpoints in . The inversion graph of a graph has the labelled orientations o…
Effect of edge-stretching on Steklov eigenvalues and sharp Steklov eigenvalue bounds on leaf--boundary trees
Jiangdong Ai, Yizhe Ji, Xiaopan Lian +1
Let be a finite tree with leaf set $\dO$ as the boundary and let be the first nontrivial Steklov eigenvalue. Let and be the maximum vertex degree and the numb…
The square of a subcubic planar graph without a 5-cycle is 7-choosable
Seog-Jin Kim, Xiaopan Lian, Atsuhiro Nakamoto +1
The square of a graph , denoted , has the same vertex set as and has an edge between two vertices if the distance between them in is at most . Thomassen [12] sho…