Jian Wang

activity

20182022

collaborators

13 papers

math.CO2022

Counterexamples to Gerbner's Conjecture on Stability of Maximal $F$ -free Graphs

Jian Wang, Shipeng Wang, Weihua Yang

Let $F$ be an $(r + 1)$ -color critical graph with $r \geq 2$ , that is, $χ (F) = r + 1$ and there is an edge $e$ in $F$ such that $χ (F - e) = r$ . Gerbner recently conjectured that every $n$ -ver…

math.CO2022

Intersections and Distinct Intersections in Cross-intersecting Families

Peter Frankl, Jian Wang

Let $F, G$ be two cross-intersecting families of $k$ -subsets of ${1, 2, \dots, n}$ . Let $F \land G$ , $I (F, G)$ d…

math.CO2021

On the sum of sizes of overlapping families

Peter Frankl, Jian Wang

Let $A_{1}, \dots, A_{m}$ be families of $k$ -subsets of an $n$ -set. Suppose that one cannot choose pairwise disjoint edges from $s + 1$ distinct families. Subject to t…

math.CO2021

The Generalized Turán Problem of Two Intersecting Cliques

Erica L. L. Liu, Jian Wang

For $s < r$ , let $B_{r, s}$ be the graph consisting of two copies of $K_{r}$ , which share exactly $s$ vertices. Denote by $e x (n, K_{r}, B_{r, s})$ the maximum number of copies of $K_{r}$ in…

math.CO2020

On the Maximum Number of Edges in Hypergraphs with Fixed Matching and Clique Number

Peter Frankl, Erica L. L. Liu, Jian Wang

For a $k$ -graph $F \subset (k [ n ])$ , the clique number of $F$ is defined to be the maximum size of a subset $Q$ of $[n]$ with $\binom{Q}{k}\subset \mathca…

math.CO2020

A Stability Theorem for Maximal $C_{2 k + 1}$ -free Graphs

Jian Wang, Shipeng Wang, Weihua Yang +1

For any positive integer $k$ , we show that every maximal $C_{2 k + 1}$ -free graph with at least $n^{2} /4 - o (n^{3/2})$ edges contains an induced complete bipartite subgraph on $(1 - o (1)) n$ …

Counterexamples to Gerbner's Conjecture on Stability of Maximal F-free Graphs