Yongtao Li

An entropy bridge from weighted to spectral Turán theorems

Yongtao Li

We establish an entropy bridge, and then use it to prove that for any color-critical graph $F$ with chromatic number $χ (F) = r + 1 \geq 3$ , there exists a constant $λ_{0} = λ_{0} (F)$ such that…

Supersaturation in Nosal graphs: Triangles and books

Hongzhang Chen, Yongtao Li, Quanyu Tang

In this paper, we use the spectral surplus $λ (G) - m$ to measure how far $G$ lies above the Nosal threshold, and prove the following edge-spectral supersaturation results fo…

An edge-spectral supersaturation of Mubayi's theorem for color-critical graphs

Hongzhang Chen, Yongtao Li

We study the supersaturation problem in its edge-spectral form. Let $λ (G)$ be the adjacency spectral radius of $G$ . Nikiforov proved that every $K_{r + 1}$ -free graph $G$ with $m$ ed…

Spectral Sidorenko inequalities and edge-spectral supersaturation

Yongtao Li, Wilson Lin, Hong Liu +1

We develop a spectral approach to Sidorenko-type inequalities and apply it to establish sharp edge-spectral supersaturation results. Let $H$ be a bipartite graph with $v$ vertices…

On a conjecture of distance spectral extremal problems

Hongzhang Chen, Jianxi Li, Yongtao Li

Brualdi and Hoffman proposed a well-known problem of determining the graph with maximum adjacency spectral radius among all graphs with given size $m$ . Early work by Friedland and…

An exponentially small gap of the Perron vector on independent sets

Hongzhang Chen, Jianxi Li, Yongtao Li +2

A classical result of Cioabă states that if $G$ is a connected graph with the unit Perron vector $x$ , then any independent set $S$ of $G$ satisfies $\sum_{v\in S} x_v^2 \l…

Subspace variations of the weighted skew Bollobás theorem

Yongjiang Wu, Yongtao Li, Lu Lu +1

Let $V$ be a finite-dimensional real vector space. A collection $P = {(A_{i}, B_{i})}_{i = 1}^{m}$ of pairs of subspaces of $V$ is called a skew Bollobás system if $\dim(A_i\cap…

More on spectral supersaturation for the bowtie

Longfei Fang, Yongtao Li, Huiqiu Lin

A central topic in extremal graph theory is the supersaturation problem, which studies the minimum number of copies of a fixed substructure that must appear in any graph with more…

Spectral supersaturation for color-critical graphs

Longfei Fang, Yongtao Li, Huiqiu Lin +1

A graph is color-critical if it contains an edge whose deletion reduces its chromatic number. This class of graphs, including cliques and odd cycles, plays a central role in extrem…

Edge-spectral Turán theorems for color-critical graphs with applications

Yongtao Li, Hong Liu, Shengtong Zhang

A classical result of Nosal asserts that every $m$ -edge graph with spectral radius $λ (G) > m$ contains a triangle. A celebrated extension of Nikiforov [2002, CPC] states that…

The product measures of cross $t$ -intersecting families

Yongjiang Wu, Yongtao Li, Zhiyi Liu +1

We investigate the product measures of intersection problems in extremal combinatorics. Invoking a recent result of He--Li--Wu--Zhang, we prove that for any $n \geq t \geq 3$ and…

Strong spectral stabilities for $C_{2 k + 1}$ -free graphs

Lantao Zou, Yongtao Li, Yuejian Peng

A stability result due to Ren, Wang, Wang and Yang [SIAM J. Discrete Math. 38 (2024)] shows that if $3 \leq r \leq 2 k$ and $n \geq 318 (r - 2)^{2} k$ , and $G$ is a $C_{2 k + 1}$ -free graph on $…

An edge-spectral Erdős-Stone-Simonovits theorem and its stability

Yongtao Li, Hong Liu, Shengtong Zhang

We study the extremal problem that relates the spectral radius $λ (G)$ of an $F$ -free graph $G$ to its number of edges. Firstly, we prove that for any graph $F$ with chromatic numbe…

math.CO2025★ 2 cited

More on Nosal's spectral theorem: Books and $4$ -cycles

Yongtao Li, Hong Liu, Shengtong Zhang

Spectral graph theory studies how the eigenvalues of a graph relate to the structural properties of a graph. In this paper, we solve three open problems in spectral extremal graph…

Non-uniform pairwise cross $t$ -intersecting families

Yongjiang Wu, Yongtao Li, Tingzeng Wu +1

Let $n \geq t \geq 1$ and $A_{1}, A_{2}, \dots, A_{m} \subseteq 2^{[n]}$ be non-empty families. We say that they are pairwise cross $t$ -intersecting if $|A…

Two results on set families: sturdiness and intersection

Yongjiang Wu, Zhiyi Liu, Lihua Feng +1

This paper resolves two open problems in extremal set theory. For a family $F \subseteq 2^{[n]}$ and $i, j \in [n]$ , we denote $\mathcal{F} (i,\bar{j})=\{F\backslash\{i\}:…

Spectral extremal problems for non-bipartite graphs without odd cycles

Lantao Zou, Lihua Feng, Yongtao Li

A well-known result of Mantel asserts that every $n$ -vertex triangle-free graph $G$ has at most $⌊ n^{2} /4 ⌋$ edges. Moreover, Erdős proved that if $G$ is further non-bip…

math.CO2025★ 2 cited

Some Turán-type results for the signless Laplacian spectral radius

Jian Zheng, Yongtao Li, Yi-Zheng Fan

Half a century ago, Bollobás and Erdős [Bull. London Math. Soc. 5 (1973)] proved that every $n$ -vertex graph $G$ with $e (G) \geq (1 - \frac{1}{k} + ε) \frac{n ^{2}}{2}$ edges c…

The signless Laplacian spectral Turán problems for color-critical graphs

Jian Zheng, Yongtao Li, Honghai Li

The well-known Turán theorem states that if $G$ is an $n$ -vertex $K_{r + 1}$ -free graph, then $e (G) \leq e (T_{n, r})$ , with equality if and only if $G$ is the $r$ -partite Turán graph $T…

Proof of Frankl's conjecture on cross-intersecting families

Yongjiang Wu, Lihua Feng, Yongtao Li

Two families $F$ and $G$ are called cross-intersecting if for every $F \in F$ and $G \in G$ , the intersection $F \cap G$ is non-empty. For any…

math.CO2024★ 1 cited

A result for hemi-bundled cross-intersecting families

Yongjiang Wu, Lihua Feng, Yongtao Li

Two families $F$ and $G$ are called cross-intersecting if for every $F \in F$ and $G \in G$ , the intersection $F \cap G$ is non-empty. It is si…

Stabilities of the Kleitman diameter theorem

Yongjiang Wu, Yongtao Li, Lihua Feng +2

Let $F$ be a family of subsets of $[n]$ . The diameter of $F$ is the maximum size of symmetric differences among pairs of its members. Resolving a conjecture of…

Maximal intersecting families revisited

Yongjiang Wu, Yongtao Li, Lihua Feng +2

The well-known Erdős--Ko--Rado theorem states that for $n > 2 k$ , every intersecting family of $k$ -sets of $[n] := {1, \dots, n}$ has at most $(k - 1 n - 1)$ sets, and the extre…