4 papers
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 Erdős and Hajnal, Chen and Ma proved that, for all , the complete bipartite graph is the unique graph on vertices with…
A complement of the Erdős-Hajnal problem on paths with equal-degree endpoints
Zhen Liu, Qinghou Zeng
Answering a question of Erdős 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 o…
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…