Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Precedence thinness in graphs   Interval and proper interval graphs are very well-known graph classes, for
which there is a wide literature. As a consequence, some generalizations of
interval graphs have been proposed, in which graphs in general are expressed in
terms of $k$ interval graphs, by splitting the graph in some special way.
  As a recent example of such an approach, the classes of $k$-thin and proper
$k$-thin graphs have been introduced generalizing interval and proper interval
graphs, respectively. The complexity of the recognition of each of these
classes is still open, even for fixed $k \geq 2$.
  In this work, we introduce a subclass of $k$-thin graphs (resp. proper
$k$-thin graphs), called precedence $k$-thin graphs (resp. precedence proper
$k$-thin graphs). Concerning partitioned precedence $k$-thin graphs, we present
a polynomial time recognition algorithm based on $PQ$-trees. With respect to
partitioned precedence proper $k$-thin graphs, we prove that the related
recognition problem is \NP-complete for an arbitrary $k$ and polynomial-time
solvable when $k$ is fixed. Moreover, we present a characterization for these
classes based on threshold graphs.

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The categories of this paper are: physics
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
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The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
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The categories of this paper are: hep-ph
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas