Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sparse spanning $k$-connected subgraphs in tournaments   In 2009, Bang-Jensen asked whether there exists a function $g(k)$ such that
every strongly $k$-connected $n$-vertex tournament contains a strongly
$k$-connected spanning subgraph with at most $kn + g(k)$ arcs. In this paper,
we answer the question by showing that every strongly $k$-connected $n$-vertex
tournament contains a strongly $k$-connected spanning subgraph with at most $kn
+ 750k^2\log(k+1)$ arcs.

7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
10
The categories of this paper are: q-bio
19
The categories of this paper are: eess
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
36
The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom