Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The logical strength of K\"onig's edge coloring theorem   K\"onig's edge coloring theorem says that a bipartite graph with maximal
degree $n$ has an edge coloring with no more than $n$ colors. We explore the
computability theory and Reverse Mathematics aspects of this theorem.
Computable bipartite graphs with degree bounded by $n$ have computable edge
colorings with $n+1$ colors, but the theorem that there is an edge coloring
with $n$ colors is equivalent to WKLo over RCAo. This gives an additional proof
of a theorem of Hirst: WKLo is equivalent over RCAo to the principle that every
countable bipartite $n$-regular graph is the union of $n$ complete matchings.
We describe open questions related to Vizing's edge coloring theorem and a
countable form of Birkhoff's theorem.

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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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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: q-fin
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: quant-ph
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The categories of this paper are: physics
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: q-bio