Xiamiao Zhao

activity

20242026

collaborators

30 papers

math.CO2026

A Vertex-Linear Threshold for Eventually Turán good and the Cluster Method

Xiamiao Zhao, Liying Kang, Yuanpei Wang

A graph $H$ is $K_{r + 1}$ -Turán-good if, for every sufficiently large $n$ , the Turán graph $T_{r} (n)$ maximizes the number of copies of $H$ among all $n$ -vertex $K_{r + 1}$ -free graphs,…

math.CO2026

Turán-good monotonicity thresholds

Yuanpei Wang, Liying Kang, Xiamiao Zhao

A graph $H$ is $K_{r + 1}$ -Turán-good if, for every sufficiently large $n$ , the Turán graph $T_{r} (n)$ maximizes the number of copies of $H$ among all $n$ -vertex $K_{r + 1}$ -free graphs.…

math.CO2026

The $(t, p)$ -Norm in Classical Extremal Problems

Xiamiao Zhao, Yuanpei Wang

Given integers $r > t \geq 1$ and a real number $p > 0$ , the $(t, p)$ -norm $∣∣ H ∣ ∣_{t, p}$ of an $r$ -graph $H$ is the sum of the $p$ -th powers of the degrees $d_{\mathcal…

math.CO2026

A stability theorem for Berge Hamiltonian cycles under a minimum degree condition

Yichen Wang, Dániel Gerbner, Xiamiao Zhao

In this paper, we study extremal and stability problems for Berge Hamiltonian cycles in $r$ -uniform hypergraphs under a minimum degree condition. Let $ g_r(n,t)=\binom{n-t}{r}+t\bi…

math.CO2026

Counting even cycles and even paths with bounded circumference

Xiamiao Zhao, Yuanpei Wang

For an integer $L$ , write $C_{\geq L}$ for the family of cycles of length at least $L$ . For $L = 2 a$ let $H (n, L) = K_{a} + K_{n - a}$ , and for $L = 2 a + 1$ let $H (n, L)$ be obtained from…

math.CO2026

Counting Cycles in Graphs with Bounded Circumference

Xiamiao Zhao, Yuanpei Wang

For an integer $L \geq 2$ , let $a = ⌊ L /2 ⌋$ . Let $H (n, L)$ be the join of $K_{a}$ and an independent set of order $n - a$ , with one extra edge in the independent set when $L$ is…

math.CO2026

Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs

Mengyu Cao, Mei Lu, Xiamiao Zhao

Let $G$ be a connected simple vertex-transitive graph on $n$ vertices with degree $d$ , and let $G_{p}$ be the random spanning subgraph obtained by retaining each edge of $G$ independ…

math.CO2026

Strong Subgraph-Count Stability in $C_{2 ℓ + 1}$ -Free Graphs

Yuanpei Wang, Xiamiao Zhao

Starting from the stability theorem of Erdős and Simonovits, stability problems for graphs forbidding a fixed subgraph have been studied in terms of edge numbers, spectral radii an…

math.NT2026

Adjacent comparison bounds and extremal sets for Ruzsa numbers

Yuchen Ding, Huixi Li, Junfeng Li +2

Let $m$ be a positive integer and $Z_{m}$ the residue class ring modulo $m$ . The Ruzsa number $R_{m}$ is defined to be the least integer $r$ such that there is a subset $\math…

math.CO2026

On the Turán number of blow-ups of $F_{5}$

Xiamiao Zhao, Xin Cheng, Dániel Gerbner +4

Let $F_{5}$ denote the $3$ -uniform hypergraph on the vertex set ${f_{1}, f_{2}, \dots, f_{5}}$ with hyperedges ${f_{1} f_{2} f_{3}, f_{1} f_{2} f_{4}, f_{3} f_{4} f_{5}}$ . Recently, Balogh, Clemen and Lu…

math.CO2026

Hypergraph extensions of the Alon--Frankl Theorem and rainbow Turán problems

Xiamiao Zhao, Yuanpei Wang, Junpeng Zhou

Given a graph $F$ , the $r$ -expansion $F^{(r) +}$ of $F$ is the $r$ -uniform hypergraph obtained from $F$ by inserting $r - 2$ new distinct vertices in each edge of $F$ . Recently, Alon…

math.CO2026

A generalization of Erdős-Hajnal problem on paths with equal-degree endpoints

Xiamiao Zhao, Yichen Wang, Mei Lu

Erdős and Hajnal proposed a problem that: is it true that every $(2 n + 1)$ -vertex graph with $n^{2} + n + 1$ edges contains two vertices of equal degree connected by a path of length three…

math.CO2026

On the connected Turán number of Berge paths and Berge cycles

Xiamiao Zhao, Dániel Gerbner, Junpeng Zhou

Given a graph $F$ , a Berge copy of $F$ (Berge- $F$ for short) is a hypergraph obtained by enlarging the edges arbitrarily. Győri, Salia and Zamora determined the maximum number of h…

math.CO2026

Generalized Turán problems for Berge hypergraphs

Xiamiao Zhao, Xin Cheng, Dániel Gerbner

Let $H$ be a hypergraph and $F$ be a graph. If there exists a bijection between the hyperedges of $H$ and the edges of $F$ such that each hyperedge contains its…

math.CO2026

The number of induced paths in outerplanar graphs

Yichen Wang, Ervin Győri, Casey Tompkins +1

Let $P_{k}$ denote the path with $k$ vertices, and $ex_{O P} (n, H^{ind}, \emptyset)$ be the maximum number of induced copies of $H$ in an $n$ -vertex outerpla…

math.CO2026

Forbidding matching as trace in uniform hypergraphs

Yichen Wang, Xin Cheng, Ervin Győri +1

We say a hypergraph $H$ contains a hypergraph $G$ as trace if there exists a vertex subset $S \subseteq V (H)$ such that $∣ S ∣ = ∣ V (G) ∣$ and $…

math.CO2026

The Turán number of the Cartesian product of a star and an edge

Xiamiao Zhao, Xin Cheng, Cheng Chi +3

Let $C_{k}$ denote the cycle of length $k$ , $S_{t}$ be a star with $t$ edges. And let $B_{t}$ be the graph consisting of $t$ copies of $C_{4}$ sharing one fixed edge. Equivalently, $B_t=K_…

math.CO2026

Forbidding edge-critical graphs as trace in uniform hypergraphs

Yichen Wang, Xin Cheng, Ervin Győri +3

We say a hypergraph $H$ contains a graph $G$ as trace if there exists a vertex subset $S \subseteq V (H)$ such that $∣ S ∣ = V (G)$ and $\{e \cap S \mid e \in E(\ma…

math.CO2026

Extremal results on Berge disjoint paths

Xiamiao Zhao, Yiyan Zhan, Mei Lu

The well-known Erdős-Gallai Theorem gave the Turán number of paths. Bushaw and Kettle generalized this result to consider the Turán number of disjoint paths. Since then, many studi…

math.CO2026

On generalized Turán problems for expansions

Junpeng Zhou, Xiamiao Zhao, Xiying Yuan

Given a graph $F$ , the $r$ -expansion $F^{r}$ of $F$ is the $r$ -uniform hypergraph obtained from $F$ by inserting $r - 2$ new distinct vertices in each edge of $F$ . Given $r$ -uniform hy…

math.CO2025

Edge version of the inducibility via the entropy method

Yichen Wang, Xiamiao Zhao, Mei Lu

The inducibility of a graph $H$ is about the maximum number of induced copies of $H$ in a graph on $n$ vertices. We consider its edge version, that is, the maximum number of induce…

math.CO2025

The Turán number of Berge matchings

Yichen Wang, Zixuan Yang, Xiamiao Zhao +2

Given a graph $F$ , an $r$ -uniform hypergraph $H$ is a {\em Berge- $F$ } if there is a bijection $ϕ : E (F) \to E (H)$ such that $e \subseteq ϕ (e)$ for each $e \in E (F)$ .…

math.CO2025

The maximum sum of sizes of non-empty cross $L$ -intersecting families

Xiamiao Zhao, Haixiang Zhang, Mei Lu

Let $n$ , $r$ , and $k$ be positive integers such that $k, r \geq 2$ , $L$ a non-empty subset of $[k]$ , and $F_{i} \subseteq (k [ n ])$ for $1 \leq i \leq r$ . We say that…

math.CO2025

Counting induced subgraphs with given intersection sizes

Haixiang Zhang, Yichen Wang, Xiamiao Zhao +1

Let $F$ be a graph of order $r$ . In this paper, we study the maximum number of induced copies of $F$ with restricted intersections, which highlights the motivation from extremal se…

A Vertex-Linear Threshold for Eventually Turán good and the Cluster Method

Turán-good monotonicity thresholds

The (t,p)-Norm in Classical Extremal Problems

A stability theorem for Berge Hamiltonian cycles under a minimum degree condition

Counting even cycles and even paths with bounded circumference

Counting Cycles in Graphs with Bounded Circumference

Matchings and Near-Optimal 2-Factor Packings in Percolated Vertex-Transitive Graphs

Strong Subgraph-Count Stability in C2ℓ+1​-Free Graphs

Adjacent comparison bounds and extremal sets for Ruzsa numbers

On the Turán number of blow-ups of F5​

Hypergraph extensions of the Alon--Frankl Theorem and rainbow Turán problems

A generalization of Erdős-Hajnal problem on paths with equal-degree endpoints

On the connected Turán number of Berge paths and Berge cycles

Generalized Turán problems for Berge hypergraphs

The number of induced paths in outerplanar graphs

Forbidding matching as trace in uniform hypergraphs

The Turán number of the Cartesian product of a star and an edge

Forbidding edge-critical graphs as trace in uniform hypergraphs

Extremal results on Berge disjoint paths

On generalized Turán problems for expansions

Edge version of the inducibility via the entropy method

The Turán number of Berge matchings

The maximum sum of sizes of non-empty cross L-intersecting families

Counting induced subgraphs with given intersection sizes

The $(t, p)$ -Norm in Classical Extremal Problems

Strong Subgraph-Count Stability in $C_{2 ℓ + 1}$ -Free Graphs

On the Turán number of blow-ups of $F_{5}$

The maximum sum of sizes of non-empty cross $L$ -intersecting families