TY - GEN

T1 - An FPT-algorithm for recognizing k-apices of minor-closed graph classes

AU - Sau, Ignasi

AU - Stamoulis, Giannos

AU - Thilikos, Dimitrios M.

N1 - Publisher Copyright:
© Ignasi Sau, Giannos Stamoulis, and Dimitrios M. Thilikos; licensed under Creative Commons License CC-BY 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020).

PY - 2020/6/1

Y1 - 2020/6/1

N2 - 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 2poly(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 2poly(k)n2 time.

AB - 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 2poly(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 2poly(k)n2 time.

KW - Graph minors

KW - Graph modification problems

KW - Irrelevant vertex technique

KW - Parameterized algorithms

UR - http://www.scopus.com/inward/record.url?scp=85089340915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85089340915&partnerID=8YFLogxK

U2 - 10.4230/LIPIcs.ICALP.2020.95

DO - 10.4230/LIPIcs.ICALP.2020.95

M3 - Conference contribution

AN - SCOPUS:85089340915

T3 - Leibniz International Proceedings in Informatics, LIPIcs

BT - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020

A2 - Czumaj, Artur

A2 - Dawar, Anuj

A2 - Merelli, Emanuela

PB - Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

T2 - 47th International Colloquium on Automata, Languages, and Programming, ICALP 2020

Y2 - 8 July 2020 through 11 July 2020

ER -