Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Finding Directed Trees with Many Leaves   The Rooted Maximum Leaf Outbranching problem consists in finding a spanning
directed tree rooted at some prescribed vertex of a digraph with the maximum
number of leaves. Its parameterized version asks if there exists such a tree
with at least $k$ leaves. We use the notion of $s-t$ numbering to exhibit
combinatorial bounds on the existence of spanning directed trees with many
leaves. These combinatorial bounds allow us to produce a constant factor
approximation algorithm for finding directed trees with many leaves, whereas
the best known approximation algorithm has a $\sqrt{OPT}$-factor. We also show
that Rooted Maximum Leaf Outbranching admits a quadratic kernel, improving over
the cubic kernel given by Fernau et al.

29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg