Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Degenerate Matchings and Edge Colorings   A matching $M$ in a graph $G$ is $r$-degenerate if the subgraph of $G$
induced by the set of vertices incident with an edge in $M$ is $r$-degenerate.
Goddard, Hedetniemi, Hedetniemi, and Laskar (Generalized subgraph-restricted
matchings in graphs, Discrete Mathematics 293 (2005) 129-138) introduced the
notion of acyclic matchings, which coincide with $1$-degenerate matchings.
Solving a problem they posed, we describe an efficient algorithm to determine
the maximum size of an $r$-degenerate matching in a given chordal graph.
Furthermore, we study the $r$-chromatic index of a graph defined as the minimum
number of $r$-degenerate matchings into which its edge set can be partitioned,
obtaining upper bounds and discussing extremal graphs.

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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: quant-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: cs
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: physics