Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Color-line and Proper Color-line Graphs   Motivated by investigations of rainbow matchings in edge colored graphs, we
introduce the notion of color-line graphs that generalizes the classical
concept of line graphs in a natural way. Let $H$ be a (properly) edge-colored
graph. The (proper) color-line graph $C\!L(H)$ of $H$ has edges of $H$ as
vertices, and two edges of $H$ are adjacent in $C\!L(H)$ if they are incident
in $H$ or have the same color. We give Krausz-type characterizations for
(proper) color-line graphs, and point out that, for any fixed $k\ge 2$,
recognizing if a graph is the color-line graph of some graph $H$ in which the
edges are colored with at most $k$ colors is NP-complete. In contrast, we show
that, for any fixed $k$, recognizing color-line graphs of properly edge colored
graphs $H$ with at most $k$ colors is polynomially. Moreover, we give a good
characterization for proper $2$-color line graphs that yields a linear time
recognition algorithm in this case.

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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: astro-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: quant-ph
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The categories of this paper are: math-ph
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The categories of this paper are: physics