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.
Keywords: complexity, caterpillar tree, graph layout problems, coloring
@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}, pages = {667--686}, publisher = {EDP-Sciences}, volume = {43}, number = {4}, year = {2009}, doi = {10.1051/ita/2009014}, mrnumber = {2589988}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ita/2009014/} }
TY - JOUR AU - Àlvarez, Carme AU - Serna, Maria TI - On the proper intervalization of colored caterpillar trees JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications PY - 2009 SP - 667 EP - 686 VL - 43 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ita/2009014/ DO - 10.1051/ita/2009014 LA - en ID - ITA_2009__43_4_667_0 ER -
%0 Journal Article %A Àlvarez, Carme %A Serna, Maria %T On the proper intervalization of colored caterpillar trees %J RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications %D 2009 %P 667-686 %V 43 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ita/2009014/ %R 10.1051/ita/2009014 %G en %F 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, Volume 43 (2009) no. 4, pp. 667-686. doi : 10.1051/ita/2009014. http://www.numdam.org/articles/10.1051/ita/2009014/
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