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This paper studies the computational complexity of the proper interval colored graph problem (picg), when the input graph
is a colored caterpillar, parameterized by hair length. In order prove our result we establish a close relationship between the picg and a graph layout problem the proper colored layout problem (pclp). We show a dichotomy: the picg and the pclp are NP-complete for colored caterpillars of hair length ≥2, while both problems are in P for colored caterpillars of hair length <2. For the hardness results we provide a reduction from the multiprocessor scheduling problem, while the polynomial time results follow from a characterization in terms of forbidden
CitationÁlvarez, M.; Serna, M. On the proper intervalization of colored caterpillar trees. "RAIRO. Theoretical informatics and applications", 2009, vol. 43, núm. 4, p. 667-686.
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