Xiutao Zhu

activity

20212026

most citedThe maximum number of triangles in

F_{k}

-free graphs

3 citations · 8 across the 21 of their papers we have counts for

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21 papers · 1 filter

math.CO2026

Near-optimal Turán densities of $r$ -graphs on $r + 1$ vertices

Jiabao Yang, Xiutao Zhu

Let $π (H)$ be the Turán density of an r-uniform hypergraph $H$ and let $H_{k}^{r}$ denote the $r$ -uniform hypergraph on $r + 1$ vertices with exactly $k$ edges, where $1 \leq k \leq r + 1$ . Si…

math.CO2026

Turán-Type Extremal Results for Distance- $k$ Graphs

Zhen He, Nika Salia, Casey Tompkins +1

We study Turán-type extremal problems for distance graphs, motivated by work of Csikvári, Bollobás, Tyomkyn, and Uzzell. We determine the maximum number of vertex pairs at distance…

math.CO2026

The Turán number of the triangular pyramid of 4-layers

Hangdi Chen, Yaojun Chen, Xiutao Zhu

The Turán number $e x (n, H)$ of a graph $H$ is the maximum number of edges in any $H$ -free graph on $n$ vertices. The triangular pyramid of $k$ -layers, denoted by $T P_{k}$ , is a genera…

math.CO2025

The Connected Bipartite Turán Problem for Long Cycles and Paths

Zhen He, Nika Salia, Xiutao Zhu

Caro, Patkós, and Tuza initiated a systematic study of the bipartite Turán number for trees, and in particular asked for the extremal number of edges in connected bipartite graphs…

math.CO2025

Sets avoiding a rainbow solution to the generalized Schur equation

Ervin Győri, Zhen He, Zequn Lv +4

A classical result in combinatorial number theory states that the largest subset of $[n]$ avoiding a solution to the equation $x + y = z$ is of size $⌈ n /2 ⌉$ . For all intege…

math.CO2025

Turán problems for suspension of a balanced tree

Xiutao Zhu, Xiaolin Wang, Yanbo Zhang +1

The Turán number $\ex(n,H)$ is the maximum number of edges that an $n$ -vertex $H$ -free graph can have. The suspension $H$ is obtained from $H$ by adding a new vertex whic…

math.CO2024

Improved bound on the number of edges of diameter- $k$ -critical graphs

Xiaolin Wang, Yanbo Zhang, Xiutao Zhu

A graph is diameter- $k$ -critical if its diameter equals $k$ and the deletion of any edge increases its diameter. The Murty-Simon Conjecture states that for any diameter-2-critical…

math.CO2024

Generalized Turán problem for a path and a clique

Xiaona Fang, Xiutao Zhu, Yaojun Chen

Let $H$ be a family of graphs. The generalized Turán number $e x (n, K_{r}, H)$ is the maximum number of copies of the clique $K_{r}$ in any $n$ -vertex $H$ -…

math.CO2023

Maximum cliques in a graph without disjoint given subgraph

Fangfang Zhang, Yaojun Chen, Ervin Gyori +1

The generalized Turán number $\ex(n,K_s,F)$ denotes the maximum number of copies of $K_{s}$ in an $n$ -vertex $F$ -free graph. Let $k F$ denote $k$ disjoint copies of $F$ . Gerbner, Meth…

math.CO2023

Extremal problems for a matching and any other graph

Xiutao Zhu, Yaojun Chen

For a family of graphs $\F$, a graph is called $\F$-free if it does not contain any member of $\F$ as a subgraph. The generalized Turán number $\ex(n,K_r,\F)$ is the maximum number…

math.CO2023★ 1 cited

A new construction for planar Turán number of cycle

Ervin Győri, Kitti Varga, Xiutao Zhu

The planar Turán number $ex_{P} (n, C_{k})$ is the largest number of edges in an $n$ -vertex planar graph with no cycle of length $k$ . Let $k \geq 11$ and $C, D$ be constan…

math.CO2022

The maximum number of cliques in graphs with bounded odd circumference

Zequn Lv, Ervin Győri, Zhen He +3

In this work, we give the sharp upper bound for the number of cliques in graphs with bounded odd circumferences. This generalized Turán-type result is an extension of the celebrate…

math.CO2022★ 1 cited

Edges not covered by monochromatic bipartite graphs

Xiutao Zhu, Ervin Győri, Zhen He +4

Let $f_{k} (n, H)$ denote the maximum number of edges not contained in any monochromatic copy of~ $H$ in a $k$ -coloring of the edges of $K_{n}$ , and let $e x (n, H)$ denote the Turán number…

math.CO2022

Generalized Turan number for the edge blow-up graph

Zequn Lv, Ervin Győri, Zhen He +4

Let $H$ be a graph and $p$ be an integer. The edge blow-up $H^{p}$ of $H$ is the graph obtained from replacing each edge in $H$ by a copy of $K_{p}$ where the new vertices of the cliqu…

math.CO2022★ 3 cited

The maximum number of triangles in $F_{k}$ -free graphs

Xiutao Zhu, Yaojun Chen, Dániel Gerbner +2

The generalized Turán number $e x (n, K_{s}, H)$ is the maximum number of complete graph $K_{s}$ in an $H$ -free graph on $n$ vertices. Let $F_{k}$ be the friendship graph consisting of $k$ t…

math.CO2022

Exact results for generalized extremal problems forbidding an even cycle

Ervin Győri, Zhen He, Zequn Lv +4

We determine the maximum number of copies of $K_{s, s}$ in a $C_{2 s + 2}$ -free $n$ -vertex graph for all integers $s \geq 2$ and sufficiently large $n$ . Moreover, for $s \in {2, 3}$ and…

math.CO2022★ 1 cited

Stability version of Dirac's theorem and its applications for generalized Turán problems

Xiutao Zhu, Ervin Győri, Zhen He +3

In 1952, Dirac proved that every $2$ -connected $n$ -vertex graph with the minimum degree $k + 1$ contains a cycle of length at least $min {n, 2 (k + 1)}$ . Here we obtain a stability ve…

math.CO2022

Turán number for odd-ballooning of trees

Xiutao Zhu, Yaojun Chen

The Turán number $e x (n, H)$ is the maximum number of edges in an $H$ -free graph on $n$ vertices. Let $T$ be any tree. The odd-ballooning of $T$ , denoted by $T_{o}$ , is a graph obtaine…

math.CO2022

The maximum number of copies of an even cycle in a planar graph

Zequn Lv, Ervin Győri, Zhen He +3

We resolve a conjecture of Cox and Martin by determining asymptotically for every $k \geq 2$ the maximum number of copies of $C_{2 k}$ in an $n$ -vertex planar graph.

math.CO2022★ 2 cited

Extremal results for graphs avoiding a rainbow subgraph

Peter Frankl, Ervin Győri, Zhen He +5

We say that $k$ graphs $G_{1}, G_{2}, \dots, G_{k}$ on a common vertex set of size $n$ contain a rainbow copy of a graph $H$ if their union contains a copy of $H$ with each edge belonging t…

math.CO2021

Generalized Turán number for linear forests

Xiutao Zhu, Yaojun Chen

The generalized Turán number $e x (n, K_{s}, H)$ is defined to be the maximum number of copies of a complete graph $K_{s}$ in any $H$ -free graph on $n$ vertices. Let $F$ be a linear forest…

Near-optimal Turán densities of r-graphs on r+1 vertices

Turán-Type Extremal Results for Distance-k Graphs

The Turán number of the triangular pyramid of 4-layers

The Connected Bipartite Turán Problem for Long Cycles and Paths

Sets avoiding a rainbow solution to the generalized Schur equation

Turán problems for suspension of a balanced tree

Improved bound on the number of edges of diameter-k-critical graphs

Generalized Turán problem for a path and a clique

Maximum cliques in a graph without disjoint given subgraph

Extremal problems for a matching and any other graph

A new construction for planar Turán number of cycle

The maximum number of cliques in graphs with bounded odd circumference

Edges not covered by monochromatic bipartite graphs

Generalized Turan number for the edge blow-up graph

The maximum number of triangles in Fk​-free graphs

Exact results for generalized extremal problems forbidding an even cycle

Stability version of Dirac's theorem and its applications for generalized Turán problems

Turán number for odd-ballooning of trees

The maximum number of copies of an even cycle in a planar graph

Extremal results for graphs avoiding a rainbow subgraph

Generalized Turán number for linear forests

Near-optimal Turán densities of $r$ -graphs on $r + 1$ vertices

Turán-Type Extremal Results for Distance- $k$ Graphs

Improved bound on the number of edges of diameter- $k$ -critical graphs

The maximum number of triangles in $F_{k}$ -free graphs