8 papers
A proof of the strong Erdős--Frankl--Füredi cover-free conjecture
Yanan Hu, Leilei Zhang
A family of nonempty sets is -cover-free if no member is contained in the union of at most other members. Let denote the least for which there is an -cover-fre…
A Sharp Ramsey Theorem for Admissible Colorings of Ordered Cliques
Yanan Hu, Zhenhua Lyu, Chenxi Yang
Let \(f(k)\) be the minimum integer \(N\) such that any red--blue edge-coloring of the ordered complete graph on \(N\) vertices contains a set of \(k\) vertices whose induced color…
Graphs with many independent vertex cuts
Yanan Hu, Xingzhi Zhan, Leilei Zhang
The cycles are the only -connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer there exist…
On the metric subgraphs of a graph
Yanan Hu, Xingzhi Zhan
The three subgraphs of a connected graph induced by the center, annulus and periphery are called its metric subgraphs. The main results are as follows. (1) There exists a graph of…
Regular homogeneously traceable nonhamiltonian graphs
Yanan Hu, Xingzhi Zhan
A graph is called homogeneously traceable if every vertex is an endpoint of a Hamilton path. In 1979 Chartrand, Gould and Kapoor proved that for every integer there exist…
On almost self-centered graphs and almost peripheral graphs
Yanan Hu, Xingzhi Zhan
An almost self-centered graph is a connected graph of order with exactly central vertices, and an almost peripheral graph is a connected graph of order with exactly $…
Possible cardinalities of the center of a graph
Yanan Hu, Xingzhi Zhan
A central vertex of a graph is a vertex whose eccentricity equals the radius. The center of a graph is the set of all central vertices. The central ratio of a graph is the ratio of…
Linear maps on nonnegative symmetric matrices preserving the independence number
Yanan Hu, Zejun Huang
The independence number of a square matrix , denoted by , is the maximum order of its principal zero submatrices. Let be the set of nonnegative symme…