7 papers · 1 filter
On a conjecture regarding the product version of the Hilton-Milner theorem
Xucheng Bu, Lihua Feng, Zejun Huang +2
Recently, Frankl and Wang considered a product version of the classical Hilton-Milner theorem. They conjectured that, if and $\mathcal{G} \subs…
Connected graphs with a large dissociation number attaining the minimum spectral radius
Zejun Huang, Chenxi Yang
A dissociation set in a graph is a subset of vertices that induces a subgraph of maximum degree at most one, which is a natural generalization of the notion of an independent set.…
Thresholds for the Frankl-Wang conjecture on maximum-degree ratios
Zejun Huang, Zhiyi Liu, Lu Lu +1
Let be an intersecting family, , and $\varrho(\mathcal{F})=Δ(\mathcal{F})/|\mathcal{F}…
Improved bound on symmetric differences of intersecting families
Lihua Feng, Zejun Huang, Qifan Wang +1
For a family , it is called intersecting if for all . We use $\mathcal{SD}(\mathcal{F}) = \{F \triangle G : F, G \in \math…
Connected graphs minimizing the spectral radius for given order and dissociation number
Zejun Huang, Jiahui Liu, Chenxi Yang
A dissociation set in a graph is a subset of vertices which induces a subgraph with maximum degree at most one. The dissociation number of a graph is the maximum cardinality of its…
The maximum number of maximum dissociation sets in potted graphs
Zejun Huang, Xinwei Zhang
A potted graph is a unicyclic graph such that its cycle contains a unique vertex with degree larger than 2. Given a graph , a subset of is a dissociation set of if it…