Galby, Esther ;
Lima, Paloma T. ;
Ries, Bernard
Reducing the Domination Number of Graphs via Edge Contractions
Abstract
In this paper, we study the following problem: given a connected graph G, can we reduce the domination number of G by at least one using k edge contractions, for some fixed integer k >= 0? We show that for k <= 2, the problem is coNP-hard. We further prove that for k=1, the problem is W[1]-hard parameterized by the size of a minimum dominating set plus the mim-width of the input graph, and that it remains NP-hard when restricted to P_9-free graphs, bipartite graphs and {C_3,...,C_{l}}-free graphs for any l >= 3. Finally, we show that for any k >= 1, the problem is polynomial-time solvable for P_5-free graphs and that it can be solved in FPT-time and XP-time when parameterized by tree-width and mim-width, respectively.
BibTeX - Entry
@InProceedings{galby_et_al:LIPIcs:2019:10985,
author = {Esther Galby and Paloma T. Lima and Bernard Ries},
title = {{Reducing the Domination Number of Graphs via Edge Contractions}},
booktitle = {44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
pages = {41:1--41:13},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-117-7},
ISSN = {1868-8969},
year = {2019},
volume = {138},
editor = {Peter Rossmanith and Pinar Heggernes and Joost-Pieter Katoen},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
address = {Dagstuhl, Germany},
URL = {http://drops.dagstuhl.de/opus/volltexte/2019/10985},
URN = {urn:nbn:de:0030-drops-109856},
doi = {10.4230/LIPIcs.MFCS.2019.41},
annote = {Keywords: domination number, blocker problem, graph classes}
}
|
Keywords: |
|
domination number, blocker problem, graph classes |
|
Seminar: |
|
44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)
|
|
Issue date: |
|
2019 |
|
Date of publication: |
|
2019 |
2019
