Partitioning graphs into connected parts

Pim van 't Hof, Daniël Paulusma, Gerhard J. Woeginger

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review

3 Citations (Scopus)


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.
Original languageEnglish
Title of host publicationComputer Science - Theory and Applications, Fourth International Computer Science Symposium in Russia, CSR 2009, Novosibirsk, Russia, August 18-23, 2009. Proceedings
EditorsAnna E. Frid, Andrey Morozov, Andrey Rybalchenko, Klaus W. Wagner
PublisherSpringer Singapore
Number of pages12
ISBN (Electronic)978-3-642-03351-3
ISBN (Print)978-3-642-03350-6
Publication statusPublished - 2009
Externally publishedYes
Event4th International Computer Science Symposium in Russia, CSR 2009 - Novosibirsk, Russian Federation
Duration: 18 Aug 200923 Aug 2009
Conference number: 4

Publication series

NameLecture Notes in Computer Science


Conference4th International Computer Science Symposium in Russia, CSR 2009
Abbreviated titleCSR 2009
CountryRussian Federation

Fingerprint Dive into the research topics of 'Partitioning graphs into connected parts'. Together they form a unique fingerprint.

Cite this