Jialin He

activity

20192026

most citedImprovements on induced subgraphs of given sizes

1 citations · 1 across the 17 of their papers we have counts for

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13 papers · 1 filter

math.CO2026

On three open problems in zero-sum Ramsey numbers

Cheng Chi, Jialin He, Quan Sun

Let $K_{N}^{(r)}$ denote the $N$ -vertex complete $r$ -uniform hypergraph. For an $r$ -uniform hypergraph $H$ and an integer $k \geq 2$ , the $k$ -color Ramsey number $R (H, k)$ is the least…

math.CO2026

A note on zero-sum Ramsey numbers of complete graphs

Cheng Chi, Jialin He, Fuhong Ma

For a graph $H$ with $3 ∣ e (H)$ , the zero-sum Ramsey number $R (H, Z_{3})$ is the least integer $N$ such that every labeling of the edges of $K_{N}$ by elements of $Z_{3}$ contains a c…

math.CO2026

On Zero-sum Ramsey numbers of complete bipartite graphs

Cheng Chi, Jialin He

For an integer $q \geq 2$ and a graph $F$ satisfying $q ∣ e (F)$ , the zero-sum Ramsey number $R (F, Z_{q})$ is the least integer $n$ such that every edge-labeling $w\colon E(K_n…

math.CO2026

On zero-sum Ramsey numbers of cycles and wheels

Cheng Chi, Jialin He

For an integer $q \geq 2$ and a graph $F$ with $q ∣ e (F)$ , let $R (F, Z_{q})$ be the least integer $n$ such that every edge-labeling $w : E (K_{n}) \to Z_{q}$ contains a copy of $F$ wh…

math.CO2026

Saturation numbers for $3$ -uniform Berge- $K_{4}$

Yihan Chen, Jialin He, Tianying Xie

The saturation number $sat_{r} (n, F)$ is the minimum number of hyperedges in an $r$ -uniform $F$ -saturated hypergraph on $n$ vertices. We determine this para…

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…

math.CO2024

Complete tripartite subgraphs of balanced tripartite graphs with large minimum degree

Yihan Chen, Jialin He, Allan Lo +3

In 1975 Bollobás, Erdős, and Szemerédi asked what minimum degree guarantees an octahedral subgraph $K_{3} (2)$ in any tripartite graph $G$ with $n$ vertices in each vertex class. We s…

math.CO2023

Counting triangles in regular graphs

Jialin He, Xinmin Hou, Jie Ma +1

In this paper, we investigate the minimum number of triangles, denoted by $t (n, k)$ , in $n$ -vertex $k$ -regular graphs, where $n$ is an odd integer and $k$ is an even integer. The we…

math.CO2022

The minimum number of clique-saturating edges

Jialin He, Fuhong Ma, Jie Ma +1

Let $G$ be a $K_{p}$ -free graph. We say $e$ is a $K_{p}$ -saturating edge of $G$ if $e \in / E (G)$ and $G + e$ contains a copy of $K_{p}$ . Denote by $f_{p} (n, e)$ the minimum number of $K_{p}$ -…

math.CO2021★ 1 cited

Improvements on induced subgraphs of given sizes

Jialin He, Jie Ma, Lilu Zhao

Given integers $m$ and $f$ , let $S_{n} (m, f)$ consist of all integers $e$ such that every $n$ -vertex graph with $e$ edges contains an $m$ -vertex induced subgraph with $f$ edges, and l…

math.CO2019

Some exact results on $4$ -cycles: stability and supersaturation

Jialin He, Jie Ma, Tianchi Yang

Extremal problems on the $4$ -cycle $C_{4}$ played a heuristic important role in the development of extremal graph theory. A fundamental theorem of Füredi states that the Turán number…

On three open problems in zero-sum Ramsey numbers

A note on zero-sum Ramsey numbers of complete graphs

On Zero-sum Ramsey numbers of complete bipartite graphs

On zero-sum Ramsey numbers of cycles and wheels

Saturation numbers for 3-uniform Berge-K4​

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

Complete tripartite subgraphs of balanced tripartite graphs with large minimum degree

Counting triangles in regular graphs

The minimum number of clique-saturating edges

Improvements on induced subgraphs of given sizes

Some exact results on 4-cycles: stability and supersaturation

Saturation numbers for $3$ -uniform Berge- $K_{4}$

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

On the $4$ -clique cover number of graphs

Some exact results on $4$ -cycles: stability and supersaturation