eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-06-29
95:1
95:20
10.4230/LIPIcs.ICALP.2020.95
article
An FPT-Algorithm for Recognizing k-Apices of Minor-Closed Graph Classes
Sau, Ignasi
1
https://orcid.org/0000-0002-8981-9287
Stamoulis, Giannos
2
3
Thilikos, Dimitrios M.
1
https://orcid.org/0000-0003-0470-1800
LIRMM, Université de Montpellier, CNRS, France
Department of Informatics and Telecommunications, National and Kapodistrian University of Athens, Greece
Inter-university Postgraduate Programme "Algorithms, Logic, and Discrete Mathematics" (ALMA), Athens, Greece
Let G be a graph class. We say that a graph G is a k-apex of G if G contains a set S of at most k vertices such that G⧵S belongs to G. We prove that if G is minor-closed, then there is an algorithm that either returns a set S certifying that G is a k-apex of G or reports that such a set does not exist, in 2^{poly(k)}n³ time. Here poly is a polynomial function whose degree depends on the maximum size of a minor-obstruction of G, i.e., the minor-minimal set of graphs not belonging to G. In the special case where G excludes some apex graph as a minor, we give an alternative algorithm running in 2^{poly(k)}n² time.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol168-icalp2020/LIPIcs.ICALP.2020.95/LIPIcs.ICALP.2020.95.pdf
Graph modification problems
irrelevant vertex technique
graph minors
parameterized algorithms