Shuang Sun

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12 papers · 1 filter

math.CO2026

A Proof of the Erdős Matching Conjecture for Large Matchings via Sharp Tail Probability for Sums of i.i.d. Nonnegative Random Variables

Cheng Chi, Shuang Sun, Yan Wang

We resolve a conjecture of Łuczak, Mieczkowska and Šileikis on the maximal tail probability of sums of independent and identically distributed nonnegative random variables. Specifi…

math.CO2026

Sharp edge-spectral supersaturation for odd cycles

Jiaqi Liu, Zhenzhen Lou, Shuang Sun

Let $G$ be a graph with $m$ edges and adjacency spectral radius$ρ(G)$, and let $N(C_{2k+1},G)$ denote the number of copies of $C_{2k+1}$ in $G$. For each fixed integer…

math.CO2026

Compactness of abundance in asymmetric hypergraph removal lemmas

Shuang Sun, Yan Wang, Yuyao Yang +1

Fix an integer $r \geq 2$ and a finite simple $r$ -uniform hypergraph $F$ with at least one edge and no isolated vertices. An $n$ -vertex $r$ -graph is $ε$ -far from being $F$ -free if at…

math.CO2026

Asymptotic Uniformity of Permanents of Random Matrices over Finite Fields of Odd Characteristic

Shuang Sun, Yuyao Yang, Jiasheng Zeng

Let $q$ be an odd prime power, and let $A_{n} = (a_{ij}) \in F_{q}^{n \times n}$ be a random matrix whose entries are independent and uniformly distributed on $F_{q}$ . The per…

math.CO2026

Every fork-free graph is perfectly weight divisible

Feng Liu, Shuang Sun, Yan Wang +2

A graph $G$ is \emph{perfectly weight divisible} if, for every positive integral weight function on $V (G)$ and every induced subgraph $H$ of $G$ with at least one edge, the vertex…

math.CO2026

Optimal coloring of ${cap, even hole}$ -free graphs with no short odd holes

Feng Liu, Shuang Sun, Yan Wang

A \emph{hole} is an induced cycle of length at least four, and an \emph{even hole} is a hole of even length. A \emph{cap} is obtained from a hole by adding a vertex adjacent to exa…

math.CO2026

A Single-Exponential Erdős--Hajnal Bound for Graphs of Bounded VC-Dimension

Shuang Sun, Yan Wang, Jiasheng Zeng

A homogeneous set in a graph is a clique or a stable set. The Erdős--Hajnal conjecture states that, for every graph $H$ , there exists $c > 0$ such that every $H$ -free graph on $n$ ve…

math.CO2026

Proofs of Two Conjectures of Alon on Subgraph Counts

Peiru Kuang, Shuang Sun, Yan Wang +1

All graphs considered are finite with no isolated vertices. Let $N (m, H)$ be the maximum number of subgraphs of a graph $G$ isomorphic to $H$ , taken over all graphs $G$ with $m$ edg…

math.CO2026

Local Turán inequalities for walks and the spectral radius

Feng Liu, Shuang Sun, Yan Wang +1

Nikiforov's well-known spectral Turán inequality for walks states that, for every graph $G$ with clique number $ω (G)$ , $λ^{r} (G) \leq w_{r} (G) (1 - 1/ ω (G))$ , where $λ (G)$ is the largest eig…

math.CO2026

Tight Bound for Nikiforov's Spectral Even-Cycle Conjecture

Peiru Kuang, Feng Liu, Shuang Sun +2

Nikiforov conjectured that, for every fixed $k \geq 2$ and all sufficiently large $n$ , the unique $n$ -vertex $C_{2 k + 2}$ -free graph with maximum adjacency spectral radius is $S^+_{n,k}…

math.CO2026

On the structures of {diamond, bowtie}-free graphs that do not contain an induced subdivision of $K_{4}$

Feng Liu, Shuang Sun, Yan Wang

A graph is $ISK_{4}$ -free if it contains no induced subdivision of $K_{4}$ . Lévêque et al. [\emph{J. Combin. Theory Ser. B} \textbf{102} (2012) 924--947] conjectured that all…

math.CO2026

On the Borodin--Kostochka conjecture for graphs with large maximum degree

Feng Liu, Shuang Sun, Yan Wang +1

The Borodin--Kostochka conjecture states that every graph $G$ with maximum degree $Δ (G) \geq 9$ satisfies $χ (G) \leq max {ω (G), Δ (G) - 1}$ . In this paper, we verify this conjecture for…

A Proof of the Erdős Matching Conjecture for Large Matchings via Sharp Tail Probability for Sums of i.i.d. Nonnegative Random Variables

Sharp edge-spectral supersaturation for odd cycles

Compactness of abundance in asymmetric hypergraph removal lemmas

Asymptotic Uniformity of Permanents of Random Matrices over Finite Fields of Odd Characteristic

Every fork-free graph is perfectly weight divisible

Optimal coloring of {cap,even hole}-free graphs with no short odd holes

A Single-Exponential Erdős--Hajnal Bound for Graphs of Bounded VC-Dimension

Proofs of Two Conjectures of Alon on Subgraph Counts

Local Turán inequalities for walks and the spectral radius

Tight Bound for Nikiforov's Spectral Even-Cycle Conjecture

On the structures of {diamond, bowtie}-free graphs that do not contain an induced subdivision of K4​

On the Borodin--Kostochka conjecture for graphs with large maximum degree

Optimal coloring of ${cap, even hole}$ -free graphs with no short odd holes

On the structures of {diamond, bowtie}-free graphs that do not contain an induced subdivision of $K_{4}$