Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The structure of typical eye-free graphs and a Turan-type result for two
  weighted colours   The $(a,b)$-eye is the graph $I_{a,b} = K_{a+b}-K_b$ obtained by deleting the
edges of a clique of size $b$ from a clique of size $a+b$. We show that for any
$a,b \ge 2$ and $p \in (0,1)$, if we condition the random graph $G \sim G(n,p)$
on having no induced copy of $I_{a,b}$, then with high probability $G$ is close
to an $a$-partite graph or the complement of a $(b-1)$-partite graph. Our proof
uses the recently developed theory of hypergraph containers, and a stability
result for an extremal problem with two weighted colours. We also apply the
stability method to obtain an exact Tur\'an-type result for this extremal
problem.

22
The categories of this paper are: chao-dyn
5
The categories of this paper are: gr-qc
0
The categories of this paper are: hep-ph
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
21
The categories of this paper are: adap-org
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
23
The categories of this paper are: solv-int
19
The categories of this paper are: eess