Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Width Parameterizations for Knot-free Vertex Deletion on Digraphs   A knot in a directed graph $G$ is a strongly connected subgraph $Q$ of $G$
with at least two vertices, such that no vertex in $V(Q)$ is an in-neighbor of
a vertex in $V(G)\setminus V(Q)$. Knots are important graph structures, because
they characterize the existence of deadlocks in a classical distributed
computation model, the so-called OR-model. Deadlock detection is correlated
with the recognition of knot-free graphs as well as deadlock resolution is
closely related to the {\sc Knot-Free Vertex Deletion (KFVD)} problem, which
consists of determining whether an input graph $G$ has a subset $S \subseteq
V(G)$ of size at most $k$ such that $G[V\setminus S]$ contains no knot. In this
paper we focus on graph width measure parameterizations for {\sc KFVD}. First,
we show that: (i) {\sc KFVD} parameterized by the size of the solution $k$ is
W[1]-hard even when $p$, the length of a longest directed path of the input
graph, as well as $\kappa$, its Kenny-width, are bounded by constants, and we
remark that {\sc KFVD} is para-NP-hard even considering many directed width
measures as parameters, but in FPT when parameterized by clique-width; (ii)
{\sc KFVD} can be solved in time $2^{O(tw)}\times n$, but assuming ETH it
cannot be solved in $2^{o(tw)}\times n^{O(1)}$, where $tw$ is the treewidth of
the underlying undirected graph. Finally, since the size of a minimum directed
feedback vertex set ($dfv$) is an upper bound for the size of a minimum
knot-free vertex deletion set, we investigate parameterization by $dfv$ and we
show that (iii) {\sc KFVD} can be solved in FPT-time parameterized by either
$dfv+\kappa$ or $dfv+p$; and it admits a Turing kernel by the distance to a DAG
having an Hamiltonian path.

27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
2
The categories of this paper are: math