Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bricks and conjectures of Berge, Fulkerson and Seymour   An $r$-graph is an $r$-regular graph where every odd set of vertices is
connected by at least $r$ edges to the rest of the graph. Seymour conjectured
that any $r$-graph is $r+1$-edge-colorable, and also that any $r$-graph
contains $2r$ perfect matchings such that each edge belongs to two of them. We
show that the minimum counter-example to either of these conjectures is a
brick. Furthermore we disprove a variant of a conjecture of Fan, Raspaud.

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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: comp-gas
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The categories of this paper are: q-alg
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The categories of this paper are: chao-dyn
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: physics
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an