Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Homogeneous Edge-Colorings of Graphs   Let G = (V, E) be a multigraph without loops and for any x {\in}V let E(x) be
the set of edges of G incident to x. A homogeneous edge-coloring of G is an
assignment of an integer m >= 2 and a coloring c:E {\to} S of the edges of
Gsuchthat|S| = mandforanyx{\in}V,if|E(x)| = mqx+rx with0 <= rx <m, there exists
a partition of E(x) in rx color classes of cardinality qx + 1 and other m-rx
color classes of cardinality qx. The homogeneous chromatic index \c{hi}(G) is
the least m for which there exists such a coloring. We determine \c{hi}(G) in
the case that G is a complete multigraph, a tree or a complete bipartite
multigraph.

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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: adap-org
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: nucl-ex
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph