Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A contribution to the second neighborhood problem   Seymour's Second Neighborhood Conjecture asserts that every digraph (without
digons) has a vertex whose first out-neighborhood is at most as large as its
second out-neighborhood. It is proved for tournaments, tournaments missing a
matching and tournaments missing a generalized star. We prove this conjecture
for classes of digraphs whose missing graph is a comb, a complete graph minus 2
independent edges, or a complete graph minus the edges of a cycle of length 5.

12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys