Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximum edge-cuts in cubic graphs with large girth and in random cubic
  graphs   We show that for every cubic graph G with sufficiently large girth there
exists a probability distribution on edge-cuts of G such that each edge is in a
randomly chosen cut with probability at least 0.88672. This implies that G
contains an edge-cut of size at least 1.33008n, where n is the number of
vertices of G, and has fractional cut covering number at most 1.127752. The
lower bound on the size of maximum edge-cut also applies to random cubic
graphs. Specifically, a random n-vertex cubic graph a.a.s. contains an edge cut
of size 1.33008n.

30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci