Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Vertex-disjoint directed and undirected cycles in general digraphs   The dicycle transversal number t(D) of a digraph D is the minimum size of a
dicycle transversal of D, i. e. a set T of vertices of D such that D-T is
acyclic. We study the following problem: Given a digraph D, decide if there is
a dicycle B in D and a cycle C in the underlying undirected graph of D such
such that B,C are disjoint. It is known that there is a polynomial time
algorithm for this problem when restricted to strongly connected graphs, which
actually finds B,C if they exist. We generalize this to any class of digraphs D
with either t(D) not equal to 1 or t(D)=1 and a bounded number of dicycle
transversals, and show that the problem is NP-complete for a special class of
digraphs D with t(D)=1 and, hence, in general.

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The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
0
The categories of this paper are: hep-ph