From the 1 of 7 linked papers with an AI index.
7 papers
A sharp asymptotic bound for odd cycles in planar graphs
Zhen Liu, Chuanshu Wu
For graphs and , let denote the number of unlabeled, not necessarily induced copies of in , and let be the maximum of…
The maximum number of paths of even length in a planar graph
Zhen Liu, Chuanshu Wu
The paper proves a conjecture giving the exact leading term for the maximum number of even‑length paths that can appear in an n‑vertex planar graph, and also resolves the Cox–Marti…
Paths of even length with equal-degree endpoints
Kaizhe Chen, Zhen Liu, Qinghou Zeng
Addressing a question posed by ErdÅs and Hajnal, Chen and Ma proved that, for all , the complete bipartite graph is the unique graph on vertices with…
Degree sequences realizing labelled -factors
Zhen Liu, Qinghou Zeng
For a positive integer \( k \), let \( [k] = \{1, 2, \ldots, k\} \). Let \( h \) be a non-negative integer, and let \( n \) be a multiple of \( h + 1 \). Define \( H \) as the disj…
Paths of length five with equal-degree endpoints
Zhen Liu, Qinghou Zeng
Addressing a question posed by ErdÅs and Hajnal, Chen and Ma proved that, for all , the complete bipartite graph is the unique graph on vertices with…
A complement of the ErdÅs-Hajnal problem on paths with equal-degree endpoints
Zhen Liu, Qinghou Zeng
Answering a question of ErdÅs and Hajnal, Chen and Ma proved that for all \(n\geq600\) every graph with \(2n + 1\) vertices and at least \(n^2 + n+1\) edges contains two vertices…