Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Forbidden induced subgraphs for graphs and signed graphs with
  eigenvalues bounded from below   The smallest eigenvalue of a graph is the smallest eigenvalue of its
adjacency matrix. We show that the family of graphs with smallest eigenvalue at
least $-\lambda$ can be defined by a finite set of forbidden induced subgraphs
if and only if $\lambda < \lambda^*$, where $\lambda^* = \beta^{1/2} +
\beta^{-1/2} \approx 2.01980$ and $\beta$ is the unique real root of $x^3 = x +
1$. This resolves a question raised by Bussemaker and Neumaier. As a byproduct,
we find all the limit points of smallest eigenvalues of graphs, supplementing
Hoffman's work on those limit points in $[-2, \infty)$.
  We also prove that the same conclusion about forbidden subgraph
characterization holds for signed graphs, and we give an application to
symmetric integer matrices whose diagonal entries are all zero. Our impetus for
the study of signed graphs is to determine the maximum cardinality of a
spherical two-distance set with two fixed angles (one acute and one obtuse) in
high dimensions. Denote by $N_{\alpha, \beta}(n)$ the maximum number of unit
vectors in $\mathbb{R}^d$ where all pairwise inner products lie in $\{\alpha,
\beta\}$ with $-1 \le \beta < 0 \le \alpha < 1$. Very recently Jiang, Tidor,
Yao, Zhang and Zhao determined the limit of $N_{\alpha, \beta}(d)/d$ as
$d\to\infty$ when $\alpha + 2\beta < 0$ or $(1-\alpha)/(\alpha-\beta) \in
\{1,\sqrt2,\sqrt3\}$, and they proposed a conjecture on the limit in terms of
eigenvalue multiplicities of signed graphs. We establish their conjecture
whenever $(1-\alpha)/(\alpha - \beta) < \lambda^*$.

26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ