Leilei Zhang

activity

20212026

most citedProof of a conjecture on hamiltonian-connected graphs

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

collaborators

19 papers

math.CO2026

A proof of the strong Erdős--Frankl--Füredi cover-free conjecture

Yanan Hu, Leilei Zhang

A family of nonempty sets is $r$ -cover-free if no member is contained in the union of at most $r$ other members. Let $T (r)$ denote the least $n$ for which there is an $r$ -cover-fre…

math.CO2026

Further Results on the Maximum Number of Stars in Graphs with Forbidden Properties

Yuxuan Liu, Jia-Bao Yang, Leilei Zhang

A graph $G$ is called $k$ -edge-hamiltonian if every linear forest (i.e., a disjoint union of paths) with at most $k$ edges is contained in a Hamilton cycle of $G$ . In 2018, Füredi,…

math.CO2026

Counterexamples to the Balogh-Linz-Patkós Conjecture

Jia-Bao Yang, Leilei Zhang

A set system $F$ is called $t$ -intersecting if $∣ A \cap B ∣ \geq t$ for every pair of sets $A, B \in F .$ A set system $F$ is $k$ -Sperner if it does not cont…

math.CO2026

On the distinct maximal-clique sizes in $k$ -uniform hypergraphs

Jiabao Yang, Lixiang Yu, Leilei Zhang

Let $g (n, k)$ be the maximum number of distinct sizes of maximal cliques in an $n$ -vertex $k$ -uniform hypergraph, and let $f (n, k) = n - g (n, k)$ . We determine the asymptotic order of $f(…

math.CO2026

The maximum number of triangles in graphs without vertex disjoint friendship graphs

Wanfang Chen, Jia-Bao Yang, Leilei Zhang

Given graphs $H$ and $F$ , the generalized Turán number $ex (n, H, F)$ is the maximum number of copies of $H$ among all $n$ -vertex $F$ -free graphs. The friendship graph $F_{k}$ …

math.CO2026

Hamiltonian Properties of 3-Connected Claw-Free Graphs and Line Graphs of 3-Hypergraphs

Kenta Ozeki, Leilei Zhang

Motivated by Thomassen's well-known line graph conjecture, many researchers have explored sufficient conditions for claw-free graphs to be Hamiltonian or Hamilton-connected. In 199…

math.CO2026

A Note on Grünbaum's Conjecture about Longest Cycles and Paths

Masaki Kashima, Kenta Ozeki, Leilei Zhang

Let $c (G)$ denote the circumference of a graph $G$ , i.e., the number of vertices in its longest cycle. For positive integers $n$ and $k$ with $n > k$ , let $Γ (n; k)$ be the cla…

math.CO2026

Stability results for Berge-matching in hypergraphs

Jia-Bao Yang, Leilei Zhang

Given a graph $F$ , a hypergraph is called a Berge- $F$ if it can be obtained by expanding each edge of $F$ into a hyperedge containing it. Let $M_{k}$ denote the matching of size $k…

math.CO2024

The minimum size of a chordal graph with given order and minimum degree

Xingzhi Zhan, Leilei Zhang

A graph is chordal if it does not contain an induced cycle of length greater than three. We determine the minimum size of a chordal graph with given order and minimum degree. In do…

math.CO2024

The maximum size of a nonhamiltonian-connected graph with given order and minimum degree

Leilei Zhang

In this paper, we determine the maximum size of a nonhamiltonian-connected graph with prescribed order and minimum degree. We also characterize the extremal graphs that attain this…

math.CO2024

Extremal problems about the order and size of nonhamiltonian locally linear graphs

Feng Liu, Leilei Zhang

The relation between local structure and global cycle properties is a classical topic in graph theory. A graph $G$ is locally linear if $G [N (v)]$ is a path for every $v \in V (G)$ . I…

math.CO2023

Further results on the number of cliques in graphs covered by long cycles

Leilei Zhang

Let $Γ (n, k)$ be the set of $2$ -connected $n$ -vertex graphs containing an edge that is not on any cycle of length at least $k + 1.$ Let $g_{s} (n, k)$ denote the maximum number of $s$ -cli…

math.CO2022

Graphs with many independent vertex cuts

Yanan Hu, Xingzhi Zhan, Leilei Zhang

The cycles are the only $2$ -connected graphs in which any two nonadjacent vertices form a vertex cut. We generalize this fact by proving that for every integer $k \geq 3$ there exist…

math.CO2022

The minimum Kirchhoff index of phenylene chains

Leilei Zhang

Let $G$ be a connected graph. The resistance distance between any two vertices of $G$ is equal to the effective resistance between them in the corresponding electrical network cons…

math.CO2022

A simple proof of Ore's theorem on the maximum size of k-connected graphs with given order and diameter

Leilei Zhang

In 1968, Ore determined the maximum size of $k$ -connected graphs with given order and diameter. In this note, we give a new short proof.

math.CO2022

The maximum number of $K_{r_{1}, \dots, r_{s}}$ in graphs with a given circumference or matching number

Leilei Zhang

Let $K_{r_{1}, \dots, r_{s}}$ denote the complete multipartite graph with class sizes $r_{1}, \dots, r_{s}$ and let $K_{s}$ denote the complete graph of order $s$ . In 2018, Luo determined the…

math.CO2021★ 1 cited

Proof of a conjecture on hamiltonian-connected graphs

Petr Vrana, Xingzhi Zhan, Leilei Zhang

We prove that every 3-connected claw-free graph with domination number at most 3 is hamiltonian-connected. The result is sharp and it is inspired by a conjecture posed by Zheng, Br…

math.CO2021

The maximum size of a graph with prescribed order, circumference and minimum degree

Leilei Zhang

Erdős determined the maximum size of a nonhamiltonian graph of order $n$ and minimum degree at least $k$ in 1962. Recently, Ning and Peng generalized. Erdős' work and gave the maxi…

math.CO2021

The maximum size of a nonhamiltonian graph with given order and connectivity

Xingzhi Zhan, Leilei Zhang

Motivated by work of Erdős, Ota determined the maximum size $g (n, k)$ of a $k$ -connected nonhamiltonian graph of order $n$ in 1995. But for some pairs $n, k,$ the maximum size is not…

A proof of the strong Erdős--Frankl--Füredi cover-free conjecture

Further Results on the Maximum Number of Stars in Graphs with Forbidden Properties

Counterexamples to the Balogh-Linz-Patkós Conjecture

On the distinct maximal-clique sizes in k-uniform hypergraphs

The maximum number of triangles in graphs without vertex disjoint friendship graphs

Hamiltonian Properties of 3-Connected Claw-Free Graphs and Line Graphs of 3-Hypergraphs

A Note on Grünbaum's Conjecture about Longest Cycles and Paths

Stability results for Berge-matching in hypergraphs

The minimum size of a chordal graph with given order and minimum degree

The maximum size of a nonhamiltonian-connected graph with given order and minimum degree

Extremal problems about the order and size of nonhamiltonian locally linear graphs

Further results on the number of cliques in graphs covered by long cycles

Graphs with many independent vertex cuts

The minimum Kirchhoff index of phenylene chains

A simple proof of Ore's theorem on the maximum size of k-connected graphs with given order and diameter

The maximum number of Kr1​,…,rs​​ in graphs with a given circumference or matching number

Proof of a conjecture on hamiltonian-connected graphs

The maximum size of a graph with prescribed order, circumference and minimum degree

The maximum size of a nonhamiltonian graph with given order and connectivity

On the distinct maximal-clique sizes in $k$ -uniform hypergraphs

The maximum number of $K_{r_{1}, \dots, r_{s}}$ in graphs with a given circumference or matching number