Quadratic Embedding Constants of Graph Joins

图的二次嵌入常数：界限与距离谱

Quadratic embedding constants of graphs: Bounds and distance spectra

本文基于Schoenberg的经典工作研究了图的二次嵌入常数（QEC），给出了树的精确上下界，揭示了QEC与距离谱的关系，并推导了图簇的QEC计算方法。

关于二部图和theta图的二次可嵌入性

On quadratic embeddability of bipartite graphs and theta graphs

本文计算了去掉不相交边的完全二部图的二次嵌入常数，并研究了theta图的二次嵌入性质，最终构造出一类无限多的非二次可嵌入原始图。

通过二次嵌入常数与团图洞察的图分类

A Classification of Graphs through Quadratic Embedding Constants and Clique Graph Insights

本文利用二次嵌入常数和团图结构对图进行分类，证明 QEC 小于 -1/2 的图具有仙人掌状结构，并给出两极大团图的 QEC 公式及满足 QEC(G)<QEC(P_5) 的图刻画。

冠状图的二次嵌入常数

Quadratic Embedding Constants of Corona Graphs

本文研究了冠状图的二次嵌入常数，推导了其计算公式，并在特定条件下给出了显式表达式。

Determining Finite Connected Graphs Along the Quadratic Embedding Constants of Paths

The QE constant of a finite connected graph $G$, denoted by $\mathrm{QEC}(G)$, is by definition the maximum of the quadratic function associated to the distance matrix on a certain sphere of codimension two. We prove that the QE constants of paths $P_n$ form a strictly increasing sequence converging to $-1/2$. Then we formulate the problem of determining all the graphs $G$ satisfying $\mathrm{QEC}(P_n)\le\mathrm{QEC}(G)<\mathrm{QEC}(P_{n+1})$. The answer is given for $n=2$ and $n=3$ by exploiting forbidden subgraphs for $\mathrm{QEC}(G)<-1/2$ and the explicit QE constants of star products of t…

Embeddings of quadratic spaces over the field of $p$-adic numbers

Nondegenerate quadratic forms over $p$-adic fields are classified by their dimension, discriminant, and Hasse invariant. This paper uses these three invariants, elementary facts about $p$-adic fields and the theory of quadratic forms to determine which types of quadratic spaces -- including degenerate cases -- can be embedded in the Euclidean $p$-adic space $(\mathbb{Q}_{p}^{n},x_{1}^{2}+\cdots+x_{n}^{2})$, and the Lorentzian space $(\mathbb{Q}_{p}^{n},x_{1}^{2}+\cdots+x_{n-1}^{2}+λx_{n}^{2})$, where $\mathbb{Q}_{p}$ is the field of $p$-adic numbers, and $λ$ is a nonsquare in the finite field …

遗传图类的联合嵌入与联合同态的不可判定性

The undecidability of joint embedding and joint homomorphism for hereditary graph classes

本文通过平铺问题归约证明了遗传图类的联合嵌入性质及联合同态性质均为不可判定，为图类理论提供了新的不可判定性结果。

扇形图与图联的二次嵌入常数

Quadratic embedding constants of fan graphs and graph joins

本文推导了图联的二次嵌入常数一般公式，并应用于扇形图，通过新多项式的最小零点给出了其常数的精确表达式与奇偶性界。

Toric 3-folds defined by quadratic binomials

Let $(X, A)$ be a polarized nonsingular toric 3-fold with not effective $A+K_X$. Then for any ample line bundle $L$ on $X$ the image of the embedding by the complete linear system of $L$ is an intersections of quadrics.

关于嵌入的Kühnel猜想的二次估计

A quadratic estimation for the Kühnel conjecture on embeddings

本文针对Kühnel猜想的高维嵌入问题，在仅有线性估计的基础上，利用几何拓扑、组合学与线性代数的交叉作用，提出了$g\ge c_k n^2$的二次估计。

关于余图和树的联合嵌入性质

On the joint embedding property for cographs and trees

针对有限禁含诱导子图所定义图族的 JEP 判定问题，论文证明在禁用 $P_4$ 时可判定，并推广到有根标号树、有界树宽和有界团宽情形。