Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Cops & Robber game on series-parallel graphs   The Cops and Robber game is played on undirected finite graphs. $k$ cops and
one robber are positioned on vertices and take turn in moving along edges. The
cops win if, after a move, a cop and the robber are on the same vertex. A graph
is called $k$-copwin, if the cops have a winning strategy.
  It is known that planar graphs are 3-copwin (Aigner & Fromme, 1984) and that
outerplanar graphs are 2-copwin (Clarke, 2002). In this short note, we prove
that series-parallel (i.e., graphs with no $K_4$ minor) graphs are 2-copwin.
  It is a well-known trick in the literature of cops & robber games to define
variants of the game which impose restrictions on the possible strategies of
the cops (see Clarke, 2002). For our proof, we define the ``cops & robber game
with exits''.
  Our proof yields a winning strategy for the cops.

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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex