7 papers · 1 filter
An exponentially small gap of the Perron vector on independent sets
Hongzhang Chen, Jianxi Li, Yongtao Li +2
A classical result of Cioabă states that if is a connected graph with the unit Perron vector , then any independent set of satisfies $\sum_{v\in S} x_v^2 \l…
An Improved Interpolation Theorem and Disproofs of Two Conjectures on 2-Connected Subgraphs
Haiyang Liu, Bo Ning
We prove that any \(2\)-connected graph \(G\) on \(n\) vertices with minimum degree \(δ(G) \ge \frac{n}{4}+2\) contains a \(2\)-connected subgraph of order \(k\) for every integer…
Exact Turán numbers of two vertex-disjoint paths
Miao Dong, Bo Ning, Long-Tu Yuan +1
The Turán number of a graph is the maximum number of edges in any graph of order that does not contain as a subgraph. In 1959, Erd\H os and Gallai obtained a sharp uppe…
Two conjectures on vertex-disjoint rainbow triangles
Xu Liu, Bo Ning, Yuting Tian
In 1963, Dirac proved that every -vertex graph has vertex-disjoint triangles if and minimum degree . The base case can be reduced t…
A new spectral Turán theorem for weighted graphs and consequences
Lele Liu, Bo Ning
Confirming a conjecture of Elphick and Edwards and strengthening a spectral theorem of Wilf, Nikiforov proved that for any -free graph , , wh…
The stability of independence polynomials of complete bipartite graphs
Guo Chen, Bo Ning, Jianhua Tu
The independence polynomial of a graph is termed {\it stable} if all its roots are located in the left half-plane , and the graph itse…