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.
@article{ITA_2009__43_4_667_0,
author = {\`Alvarez, Carme and Serna, Maria},
title = {On the proper intervalization of colored caterpillar trees},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
volume = {43},
year = {2009},
pages = {667-686},
doi = {10.1051/ita/2009014},
mrnumber = {2589988},
zbl = {pre05650343},
language = {en},
url = {http://dml.mathdoc.fr/item/ITA_2009__43_4_667_0}
}
Àlvarez, Carme; Serna, Maria. On the proper intervalization of colored caterpillar trees. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 43 (2009) pp. 667-686. doi : 10.1051/ita/2009014. http://gdmltest.u-ga.fr/item/ITA_2009__43_4_667_0/
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