Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The diamond-free process   Let K_4^- denote the diamond graph, formed by removing an edge from the
complete graph K_4. We consider the following random graph process: starting
with n isolated vertices, add edges uniformly at random provided no such edge
creates a copy of K_4^-. We show that, with probability tending to 1 as $n \to
\infty$, the final size of the graph produced is $\Theta(\sqrt{\log(n)} \cdot
n^{3/2})$. Our analysis also suggests that the graph produced after i edges are
added resembles the random graph, with the additional condition that the edges
which do not lie on triangles form a random-looking subgraph.

36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas