E. Liu

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20192021

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4 papers · 1 filter

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

The Maximum Number of Cliques in Hypergraphs without Large Matchings

Erica L. L. Liu, Jian Wang

Let $[n]$ denote the set ${1, 2, \dots, n}$ and $F_{n, k, a}^{(r)}$ be an $r$ -uniform hypergraph on the vertex set $[n]$ with edge set consisting of all the $r$ -element…

math.CO2019

Turán Problems for Vertex-disjoint Cliques in Multi-partite Hypergraphs

Erica L. L. Liu, Jian Wang

For two $s$ -uniform hypergraphs $H$ and $F$ , the Turán number $e x_{s} (H, F)$ is the maximum number of edges in an $F$ -free subgraph of $H$ . Let $s, r, k, n_{1}, \dots, n_{r}$ be integers…