Menglong Zhang

activity

20232026

collaborators

Showing math.COShow all

6 papers · 1 filter

math.CO2026

Erdős-Ko-Rado-type problem for hypergraph matchings

Binwei Zhao, Tao Feng, Xiaomiao Wang +1

Given integers $1 \leq t \leq k$ , a family of $k$ -matchings in a complete $r$ -partite $r$ -uniform hypergraph is said to be $t$ -intersecting if any two of its members share at least $…

math.CO2025

Perfect difference families, perfect systems of difference sets and their applications

Hengrui Liu, Tao Feng, Xiaomiao Wang +1

Let $v$ be a positive odd integer. A $(v, k, λ)$ -perfect difference family (PDF) is a collection $F$ of $k$ -subsets of ${0, 1, \dots, v - 1}$ such that the multiset $\bigcup_…

math.CO2025

Progress towards generalized Nash-Williams' conjecture on $K_{4}$ -decompositions

Menglong Zhang, Gennian Ge

A $K_{4}$ -decomposition of a graph is a partition of its edges into $K_{4}$ s. A fractional $K_{4}$ -decomposition is an assignment of a nonnegative weight to each $K_{4}$ in a graph such th…

math.CO2024

The asymptotic existence of BIBDs having a nesting

Xinyue Ming, Tao Feng, Menglong Zhang

A $(v, k, λ)$ -BIBD $(X, B)$ can be nested if there is a mapping $ϕ : B \to X$ such that $(X, {B \cup {ϕ (B)} ∣ B \in B})$ is a $(v, k + 1, λ + 1)$ -packing. A…

math.CO2023

Cyclic relative difference families with block size four and their applications

Chenya Zhao, Binwei Zhao, Yanxun Chang +3

Given a subgroup $H$ of a group $(G, +)$ , a $(G, H, k, 1)$ difference family (DF) is a set $F$ of $k$ -subsets of $G$ such that $\{f-f':f,f'\in F, f\neq f',F\in \mathcal F\}=G\…

math.CO2023

A note on non-empty cross-intersecting families

Menglong Zhang, Tao Feng

The families $F_{1} \subseteq (k _{1} [ n ]), F_{2} \subseteq (k _{2} [ n ]), \dots, F_{r} \subseteq (k _{r} [ n ])$ are said to be cross-intersecting if $|F_i…