On the proper intervalization of colored caterpillar trees
Carme Àlvarez, Marı́a Serna · RAIRO - Theoretical Informatics and Applications · 2009
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 subgraphs.