Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Thresholds in random motif graphs   We introduce a natural generalization of the Erd\H{o}s-R\'enyi random graph
model in which random instances of a fixed motif are added independently. The
binomial random motif graph $G(H,n,p)$ is the random (multi)graph obtained by
adding an instance of a fixed graph $H$ on each of the copies of $H$ in the
complete graph on $n$ vertices, independently with probability $p$. We
establish that every monotone property has a threshold in this model, and
determine the thresholds for connectivity, Hamiltonicity, the existence of a
perfect matching, and subgraph appearance. Moreover, in the first three cases
we give the analogous hitting time results; with high probability, the first
graph in the random motif graph process that has minimum degree one (or two) is
connected and contains a perfect matching (or Hamiltonian respectively).

28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int