The Proper interval colored graph problem for caterpillar trees

This paper studies the computational complexity of the Proper Interval Colored Graph problem (PICG), when the input graph is a colored tree. We show that the problem is hard for the class of caterpillar trees. To prove our result we make use of a close relationship between intervalizing problems and graph layout problems. We define a graph layout problem the Proper Colored Layout Problem (PCLP). Although PCLP is not equivalent to PICG, by transforming the input graph we will stablish a close relationship between both problems. The main result is that the PICG is NP-complete for colored caterpillars of hair length 2 and in P for caterpillars of hair length 1 or 0.Postprint (published version

The Proper Interval Colored Graph problem for caterpillar trees

This paper studies the computational complexity of the Proper interval colored graph problem (picg), when the input graph is a colored tree. We show that the problem is hard for the class of caterpillar trees. To prove our result we make use of a close relationship between intervalizing problems and graph layout problems. We define a graph layout problem the Proper colored layout problem (pclp). Although the pclp is not equivalent to the picg, by transforming the input graph we will establish a close relationship between both problems. The main result is that the picg is NP-complete for colored caterpillars of hair length 2 and in P for caterpillars of hair length 1 or 0. This research was partially supported by the ESPRIT Long Term Research Project no. 20244 -- ALCOMIT, CICYT project TIC97-1475-CE, SGR: CIRIT 1997SGR-00366 and KOALA: DGES PB95-0787. y Departament de Llenguatges i Sistemes Inform`atics, Universitat Polit`ecnica Catalunya, Edifici C6 Campus Nord, Jordi Girona Salga..