Bo Ning

collaborators

4 papers

math.CO2025

Exact Turán numbers of two vertex-disjoint paths

Miao Dong, Bo Ning, Long-Tu Yuan +1

The Turán number of a graph $H$ is the maximum number of edges in any graph of order $n$ that does not contain $H$ as a subgraph. In 1959, Erd\H os and Gallai obtained a sharp uppe…

math.CO2025

Two conjectures on vertex-disjoint rainbow triangles

Xu Liu, Bo Ning, Yuting Tian

In 1963, Dirac proved that every $n$ -vertex graph has $k$ vertex-disjoint triangles if $n \geq 3 k$ and minimum degree $δ (G) \geq \frac{n + k}{2}$ . The base case $n = 3 k$ can be reduced t…

math.CO2025

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 $K_{r + 1}$ -free graph $G$ , $λ (G)^{2} \leq 2 (1 - 1/ r) m$ , wh…

math.CO2025

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 ${z \in C : Re (z) \leq 0}$ , and the graph itse…