کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
436820 | 690041 | 2007 | 12 صفحه PDF | دانلود رایگان |

Extending previous NP-completeness results for the harmonious coloring problem and the pair-complete coloring problem on trees, bipartite graphs and cographs, we prove that these problems are also NP-complete on connected bipartite permutation graphs. We also study the k-path partition problem and, motivated by a recent work of Steiner [G. Steiner, On the k-path partition of graphs, Theoret. Comput. Sci. 290 (2003) 2147–2155], where he left the problem open for the class of convex graphs, we prove that the k-path partition problem is NP-complete on convex graphs. Moreover, we study the complexity of these problems on two well-known subclasses of chordal graphs namely quasi-threshold and threshold graphs. Based on the work of Bodlaender [H.L. Bodlaender, Achromatic number is NP-complete for cographs and interval graphs, Inform. Process. Lett. 31 (1989) 135–138], we show NP-completeness results for the pair-complete coloring and harmonious coloring problems on quasi-threshold graphs. Concerning the k-path partition problem, we prove that it is also NP-complete on this class of graphs. It is known that both the harmonious coloring problem and the k-path partition problem are polynomially solvable on threshold graphs. We show that the pair-complete coloring problem is also polynomially solvable on threshold graphs by describing a linear-time algorithm.
Journal: Theoretical Computer Science - Volume 381, Issues 1–3, 22 August 2007, Pages 248-259