Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Octal Games on Graphs: The game 0.33 on subdivided stars and bistars   Octal games are a well-defined family of two-player games played on heaps of
counters, in which the players remove alternately a certain number of counters
from a heap, sometimes being allowed to split a heap into two nonempty heaps,
until no counter can be removed anymore. We extend the definition of octal
games to play them on graphs: heaps are replaced by connected components and
counters by vertices. Thus, an octal game on a path P\_n is equivalent to
playing the same octal game on a heap of n counters. We study one of the
simplest octal games, called 0.33, in which the players can remove one vertex
or two adjacent vertices without disconnecting the graph. We study this game on
trees and give a complete resolution of this game on subdivided stars and
bistars.

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The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio
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The categories of this paper are: physics
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex