Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Merging Combinatorial Design and Optimization: the Oberwolfach Problem   The Oberwolfach Problem $OP(F)$ -- posed by Gerhard Ringel in 1967 -- is a
paradigmatic Combinatorial Design problem asking whether the complete graph
$K_v$ decomposes into edge-disjoint copies of a $2$-regular graph $F$ of order
$v$. In this paper, we provide all the necessary equipment to generate
solutions to $OP(F)$ for relatively small orders by using the so-called
difference methods. From the theoretical standpoint, we present new insights on
the combinatorial structures involved in the solution of the problem.
Computationally, we provide a full recipe whose base ingredients are advanced
optimization models and tailored algorithms. This algorithmic arsenal can solve
the $OP(F)$ for all possible orders up to $60$ with the modest computing
resources of a personal computer. The new $20$ orders, from $41$ to $60$,
encompass $241200$ instances of the Oberwolfach Problem, which is 22 times
greater than those solved in previous contributions.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: patt-sol
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The categories of this paper are: supr-con
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: hep-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: stat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-lat
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The categories of this paper are: eess
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The categories of this paper are: math-ph