Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Maximal and maximum transitive relation contained in a given binary
  relation   We study the problem of finding a \textit{maximal} transitive relation
contained in a given binary relation. Given a binary relation of size $m$
defined on a set of size $n$, we present a polynomial time algorithm that finds
a maximal transitive sub-relation in time $O(n^2 + nm)$.
  We also study the problem of finding a \textit{maximum} transitive relation
contained in a binary relation. This is the problem of computing a maximum
transitive subgraph in a given digraph. For the class of directed graphs with
the underlying graph being triangle-free, we present a $0.874$-approximation
algorithm. This is achieved via a simple connection to the problem of maximum
directed cut. Further, we give an upper bound for the size of any maximum
transitive relation to be $m/4 + cm^{4/5}$, where $c > 0$ and $m$ is the number
of edges in the digraph.

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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph