3 papers
math.CO2026
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…
math.CO2025
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…
math.CO2025
Equating three degrees of graphs
Zhen Liu, Qinghou Zeng
In this paper, we prove that, for every graph with at least 5 vertices, one can delete at most 3 vertices such that the subgraph obtained has at least three vertices with the same…