Jialin He

collaborators

3 papers

math.CO2025

On the number of triangles in $K_{4}$ -free graphs

Jialin He, Jie Ma, Yan Wang +1

Erdős asked whether for any $n$ -vertex graph $G$ , the parameter $p^{*} (G) = min \sum_{i \geq 1} (∣ V (G_{i}) ∣ - 1)$ is at most $⌊ n^{2} /4 ⌋$ , where the minimum is taken over all edge…

math.CO2025

On the $4$ -clique cover number of graphs

Yihan Chen, Jialin He, Tianying Xie

In 1966, Erdős, Goodman, and Pósa proved that $⌊ n^{2} /4 ⌋$ cliques are sufficient to cover all edges in any $n$ -vertex graph, with tightness achieved by the balanced com…

math.CO2024

Clique covers and decompositions of cliques of graphs

József Balogh, Jialin He, Robert A. Krueger +2

In 1966, Erdős, Goodman, and Pósa showed that if $G$ is an $n$ -vertex graph, then at most $⌊ n^{2} /4 ⌋$ cliques of $G$ are needed to cover the edges of $G$ , and the bound…

On the number of triangles in K4​-free graphs

On the 4-clique cover number of graphs

Clique covers and decompositions of cliques of graphs

On the number of triangles in $K_{4}$ -free graphs

On the $4$ -clique cover number of graphs