Erfei Yue

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7 papers · 1 filter

math.CO2025

Some results on minimum saturated graphs

Chenke Zhang, Qing Cui, Jinze Hu +2

Let $G$ be a graph and $F$ be a family of graphs. We say a graph $G$ is $F$ -saturated if $G$ does not contain any member in $F$ and for any $e\in E(\o…

math.CO2025

Poset saturation of unions of chains

Shengjin Ji, Balázs Patkós, Erfei Yue

A family $G$ of sets is a(n induced) copy of a poset $P = (P, ⩽)$ if there exists a bijection $b : P \to G$ such that $p ⩽ q$ holds if and only…

math.CO2024

On Bollobás-type theorems of $d$ -tuples

Erfei Yue

In 1965, Bollobás proved that for a Bollobás set-pair system ${(A_{i}, B_{i}) ∣ i \in [m]}$ , the maximum value of $\sum_{i = 1}^{m} (A _{i} ∣ A _{i} ∣ + ∣ B _{i} ∣)^{- 1}$ is $1$ . Hegedüs and Frank…

math.CO2024

A Bollobáss-type theorem on singular linear spaces

Erfei Yue, Benjian Lv, Péter Sziklai +1

Bollobás-type theorem determines the maximum cardinality of a Bollobás system of sets. The original result has been extended to various mathematical structures beyond sets, includi…

math.CO2024

The maximum sum of the sizes of all intersections within $m$ -size families

Sumin Huang, Gyula O. H. Katona, Erfei Yue

For a family of sets $F$ , let $ω (F) := \sum_{{A, B} \subset F} ∣ A \cap B ∣$ . In this paper, we prove that provided $n$ is sufficiently large, for any $\mat…

math.CO2024

Some new Bollobás-type inequalities

Erfei Yue

A family of disjoint pairs of finite sets $P = {(A_{i}, B_{i}) ∣ i \in [m]}$ is called a Bollobás system if $A_{i} \cap B_{j} \neq = \emptyset$ for every $i \neq = j$ , and a skew Bollobás…

Some results on minimum saturated graphs

Poset saturation of unions of chains

On Bollobás-type theorems of d-tuples

A Bollobáss-type theorem on singular linear spaces

The maximum sum of the sizes of all intersections within m-size families

Some new Bollobás-type inequalities

On Bollobás-type theorems of $d$ -tuples

The maximum sum of the sizes of all intersections within $m$ -size families