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DOI: 10.4230/LIPIcs.ISAAC.2020.22
URN: urn:nbn:de:0030-drops-133664
URL: https://drops.dagstuhl.de/opus/volltexte/2020/13366/
Kern, Walter ; Paulusma, Daniël
Contracting to a Longest Path in H-Free Graphs
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Abstract
The Path Contraction problem has as input a graph G and an integer k and is to decide if G can be modified to the k-vertex path P_k by a sequence of edge contractions. A graph G is H-free for some graph H if G does not contain H as an induced subgraph. The Path Contraction problem restricted to H-free graphs is known to be NP-complete if H = claw or H = P₆ and polynomial-time solvable if H = P₅. We first settle the complexity of Path Contraction on H-free graphs for every H by developing a common technique. We then compare our classification with a (new) classification of the complexity of the problem Long Induced Path, which is to decide for a given integer k, if a given graph can be modified to P_k by a sequence of vertex deletions. Finally, we prove that the complexity classifications of Path Contraction and Cycle Contraction for H-free graphs do not coincide. The latter problem, which has not been fully classified for H-free graphs yet, is to decide if for some given integer k, a given graph contains the k-vertex cycle C_k as a contraction.
BibTeX - Entry
@InProceedings{kern_et_al:LIPIcs:2020:13366,
author = {Walter Kern and Dani{\"e}l Paulusma},
title = {{Contracting to a Longest Path in H-Free Graphs}},
booktitle = {31st International Symposium on Algorithms and Computation (ISAAC 2020)},
pages = {22:1--22:18},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-173-3},
ISSN = {1868-8969},
year = {2020},
volume = {181},
editor = {Yixin Cao and Siu-Wing Cheng and Minming Li},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/13366},
URN = {urn:nbn:de:0030-drops-133664},
doi = {10.4230/LIPIcs.ISAAC.2020.22},
annote = {Keywords: dichotomy, edge contraction, path, cycle, H-free graph}
}
| Keywords: | dichotomy, edge contraction, path, cycle, H-free graph | |
| Seminar: | 31st International Symposium on Algorithms and Computation (ISAAC 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 04.12.2020 |
