Jian Wang

activity

20182026

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16 papers · 1 filter

math.CO2026

Intersecting families with covering number three II

Peter Frankl, Jian Wang

A family $F \subset (k [ n ])$ is called intersecting if $F \cap F^{'} \neq = \emptyset$ for all $F, F^{'} \in F$ . The covering number of a family $F$ is defi…

math.CO2023

A stability result for $C_{2 k + 1}$ -free graphs

Sijie Ren, Jian Wang, Shipeng Wang +1

A graph $G$ is called $C_{2 k + 1}$ -free if it does not contain any cycle of length $2 k + 1$ . In 1981, Haggkvist, Faudree and Schelp showed that every $n$ -vertex triangle-free graph wit…

math.CO2022

Improved bounds concerning the maximum degree of intersecting hypergraphs

Peter Frankl, Jian Wang

For positive integers $n > k > t$ let $(k [ n ])$ denote the collection of all $k$ -subsets of the standard $n$ -element set $[n] = {1, \dots, n}$ . Subsets of $(k [ n ])$ are ca…

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…

Intersecting families with covering number three II

A stability result for C2k+1​-free graphs

Improved bounds concerning the maximum degree of intersecting hypergraphs

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

Intersections and Distinct Intersections in Cross-intersecting Families

On the sum of sizes of overlapping families

A stability result for $C_{2 k + 1}$ -free graphs

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