@inproceedings{1a40120031c1496ebfb11db6ace73881,

title = "Partitioning graphs into connected parts",

abstract = "The 2-DISJOINT CONNECTED SUBGRAPHS problem asks if a given graph has two vertex-disjoint connected subgraphs containing pre-specified sets of vertices. We show that this problem is NP-complete even if one of the sets has cardinality 2. The LONGEST PATH CONTRACTIBILITY problem asks for the largest integer l for which an input graph can be contracted to the path P l on l vertices. We show that the computational complexity of the LONGEST PATH CONTRACTIBILITY problem restricted to P l-free graphs jumps from being polynomially solvable to being NP-hard at l=¿6, while this jump occurs at l=¿5 for the 2-DISJOINT CONNECTED SUBGRAPHS problem. We also present an exact algorithm that solves the 2-DISJOINT CONNECTED SUBGRAPHS problem faster than O*(2n) for any n-vertex P l-free graph. For l=¿6, its running time is O*(1.5790n). We modify this algorithm to solve the LONGEST PATH CONTRACTIBILITY problem for P 6-free graphs in O*(1.5790n) time.",

author = "{Hof, van 't}, P. and D. Paulusma and G.J. Woeginger",

year = "2009",

doi = "10.1007/978-3-642-03351-3_15",

language = "English",

isbn = "978-3-642-03350-6",

series = "Lecture Notes in Computer Science",

publisher = "Springer",

pages = "143--154",

editor = "A. Frid and A.S. Morozov and A. Rybalchenko and K.W. Wagner",

booktitle = "Computer Science: Theory and Applications (Fourth International Computer Science Symposium in Russia, CSR 2009, Novosibirsk, Russia, August 18-23, 2009, Proceedings)",

address = "Germany",

}