Jiangdong Ai

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20242026

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12 papers · 1 filter

math.CO2026

An improved finite bound for oriented trees in tournaments

Jiangdong Ai, Xiaopan Lian

Sumner's universal tournament conjecture asserts that every tournament on $2 n - 2$ vertices contains every oriented tree on $n$ vertices. Let $f (n)$ be the least integer $N$ such tha…

math.CO2026

Tree suspensions and transfer functions for single degree Turán spectra

Jiangdong Ai, Laihao Ding, Hong Liu +1

For integers $1 \leq ℓ < k$ , let $Π_{ℓ}^{k}$ denote the single-forbidden $ℓ$ -degree Turán spectrum of $k$ -uniform hypergraphs. We introduce transfer functions for this spectrum: e…

math.CO2026

Maximizing the Steklov eigenvalues on trees with a diameter constraint

Jiangdong Ai, Huiqiu Lin, Yongtang Shi

We study the first nonzero Steklov eigenvalue $λ_{2} (T, δ Ω)$ of the Dirichlet-to-Neumann operator on a finite tree $T$ with leaf boundary $δ Ω$ , under a constraint on the diameter $D$ .…

math.CO2026

Effect of edge-stretching on Steklov eigenvalues and sharp Steklov eigenvalue bounds on leaf--boundary trees

Jiangdong Ai, Yizhe Ji, Xiaopan Lian +1

Let $T$ be a finite tree with leaf set $\dO$ as the boundary and let $λ_{2}$ be the first nontrivial Steklov eigenvalue. Let $D$ and $ℓ$ be the maximum vertex degree and the numbe…

math.CO2026

Refinements of Alon-Babai-Suzuki-type intersection theorems via non-shadows and binomial support

Jiangdong Ai, Mingyu Liu

We prove a multilevel non-shadow refinement of the Alon--Babai--Suzuki (ABS) nonuniform restricted-intersection theorem. Let $K = {k_{1}, \dots, k_{r}}$ and let $L$ be a set with $∣ L ∣ = s$ …

math.CO2026

Vanishing orders, suspensions and zero degree Turán densities

Jiangdong Ai, Laihao Ding, Hong Liu +1

For integers $1 \leq ℓ < k$ , the $ℓ$ -degree Turán density $π_{ℓ} (F)$ measures the minimum $ℓ$ -degree threshold that forces a copy of a fixed $k$ -uniform hypergraph $F$ , gener…

math.CO2026

Triangular cutoff threshold for the inversion walk on tournaments and the state space of restricted inversions

Jiangdong Ai

Given a labelled tournament on $[n]$ , \emph{inverting} a vertex subset $X$ means reversing every edge with both endpoints in $X$ . Alon, Powierski, Savery, Scott, and Wilmer~\cite{A…

math.CO2025

Strong Ramsey game on two boards

Jiangdong Ai, Jun Gao, Zixiang Xu +1

The strong Ramsey game $R (B, H)$ is a two-player game played on a graph $B$ , referred to as the board, with a target graph $H$ . In this game, two players, $P_{1}$ …

math.CO2024

Spanning weakly even trees of graphs

Jiangdong Ai, M. N. Ellingham, Zhipeng Gao +5

Let $G$ be a graph (with multiple edges allowed) and let $T$ be a tree in $G$ . We say that $T$ is $even$ if every leaf of $T$ belongs to the same part of the bipartition o…

math.CO2024

A short note on spanning even trees

Jiangdong Ai, Zhipeng Gao, Xiangzhou Liu +1

We call a tree $T$ is \emph{even} if every pair of its leaves is joined by a path of even length. Jackson and Yoshimoto~[J. Graph Theory, 2024] conjectured that every $r$ -regular n…

math.CO2024

A variable version of the quasi-kernel conjecture

Jiangdong Ai, Xiangzhou Liu, Fei Peng

A quasi-kernel of a digraph $D$ is an independent set $Q$ such that every vertex can reach $Q$ in at most two steps. A 48-year conjecture made by P.L. Erdős and Székely, denoted th…

math.CO2024

Piercing independent sets in graphs without large induced matching

Jiangdong Ai, Hong Liu, Zixiang Xu +1

Given a graph $G$ , denote by $h (G)$ the smallest size of a subset of $V (G)$ which intersects every maximum independent set of $G$ . We prove that any graph $G$ without induced match…