Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Period Lengths of the Parallel Chip-Firing Game   The parallel chip-firing game is a periodic automaton on graphs in which
vertices "fire" chips to their neighbors. In 1989, Bitar conjectured that the
period of a parallel chip-firing game with n vertices is at most n. Though this
conjecture was disproven in 1994 by Kiwi et. al., it has been proven for
particular classes of graphs, specifically trees (Bitar and Goles, 1992) and
the complete graph K_n (Levine, 2008). We prove Bitar's conjecture for complete
bipartite graphs and characterize completely all possible periods for positions
of the parallel chip-firing game on such graphs. Furthermore, we extend our
construction of all possible periods for games on the bipartite graph to games
on complete c-partite graphs, c>2, and prove some pertinent lemmas about games
on general simple connected graphs.

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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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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: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org