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An FPT-Algorithm for Recognizing k-Apices of Minor-Closed Graph Classes
Abstract : 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) n 3 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) n 2 time.
Cited literature [51 references]
https://hal-lirmm.ccsd.cnrs.fr/lirmm-02991704
Contributor : Isabelle Gouat <>
Submitted on : Friday, November 6, 2020 - 10:06:49 AM
Last modification on : Monday, December 14, 2020 - 5:27:16 PM
Long-term archiving on: : Sunday, February 7, 2021 - 6:26:49 PM
Contributor : Isabelle Gouat <>
Submitted on : Friday, November 6, 2020 - 10:06:49 AM
Last modification on : Monday, December 14, 2020 - 5:27:16 PM
Long-term archiving on: : Sunday, February 7, 2021 - 6:26:49 PM
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LIPIcs-ICALP-2020-95.pdf
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