On the proper intervalization of colored caterpillar trees

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.Preprin

On the proper intervalization of colored caterpillar trees

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

On the proper intervalization of colored caterpillar trees

This paper studies the computational complexity of the proper interval colored graph problem (PIC

On the proper intervalization of colored caterpillar trees

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