Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposing tournaments into paths   We consider a generalisation of Kelly's conjecture which is due to Alspach,
Mason, and Pullman from 1976. Kelly's conjecture states that every regular
tournament has an edge decomposition into Hamilton cycles, and this was proved
by K\"uhn and Osthus for large tournaments. The conjecture of Alspach, Mason,
and Pullman asks for the minimum number of paths needed in a path decomposition
of a general tournament $T$. There is a natural lower bound for this number in
terms of the degree sequence of $T$ and it is conjectured that this bound is
correct for tournaments of even order. Almost all cases of the conjecture are
open and we prove many of them.

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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: nucl-ex
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys