Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterizing DAG-depth of Directed Graphs   We study DAG-depth, a structural depth measure of directed graphs, which
naturally extends the tree-depth of ordinary graphs. We define a DAG-depth
decomposition as a strategy for the cop player in the lift-free version of the
cops-and-robber game on directed graphs and prove its correctness. The
DAG-depth decomposition is related to DAG-depth in a similar way as an
elimination tree is related to the tree-depth. We study the size aspect of
DAG-depth decomposition and provide a definition of mergeable and optimally
mergeable vertices in order to make the decomposition smaller and acceptable
for the cop player as a strategy. We also provide a way to find the closure of
a DAG-depth decomposition, which is the largest digraph for which the given
decomposition represents a winning strategy for the cop player.

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The categories of this paper are: cond-mat
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
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The categories of this paper are: eess
37
The categories of this paper are: supr-con
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: econ