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An FPT Algorithm and a Polynomial Kernel for Linear Rankwidth-1 Vertex Deletion

hal.structure.identifier
dc.contributor.authorPaul, Christophe
HAL ID: 4726
hal.structure.identifierLaboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
dc.contributor.authorKim, Eun Jung
hal.structure.identifier
dc.contributor.authorKanté, Mamadou Moustapha
HAL ID: 172339
ORCID: 0000-0003-1838-7744
hal.structure.identifier
dc.contributor.authorKwon, O-joung
dc.date.accessioned2020-09-30T10:08:30Z
dc.date.available2020-09-30T10:08:30Z
dc.date.issued2015
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/21021
dc.language.isoenen
dc.subject(linear) rankwidthen
dc.subjectDistance-hereditary graphsen
dc.subjectThread graphsen
dc.subjectParameterized complexityen
dc.subjectKernelizationen
dc.subject.ddc511en
dc.titleAn FPT Algorithm and a Polynomial Kernel for Linear Rankwidth-1 Vertex Deletionen
dc.typeCommunication / Conférence
dc.description.abstractenLinear rankwidth is a linearized variant of rankwidth, introduced by Oum and Seymour [Approxi-mating clique-width and branch-width. J. Combin. Theory Ser. B, 96(4):514-528, 2006.], and it is similar to pathwidth, which is the linearized variant of treewidth. Motivated from the results on graph modification problems into graphs of bounded treewidth or pathwidth, we investigate a graph modification problem into the class of graphs having linear rankwidth at most one, called the Linear Rankwidth-1 Vertex Deletion (shortly, LRW1-Vertex Deletion). In this problem, given an n-vertex graph G and a positive integer k, we want to decide whether there is a set of at most k vertices whose removal turns G into a graph of linear rankwidth at most one and if one exists, find such a vertex set. While the meta-theorem of Courcelle, Makowsky, and Rotics implies that LRW1-Vertex Deletion can be solved in time f (k) · n 3 for some function f , it is not clear whether this problem allows a runtime with a modest exponential function. We establish that LRW1-Vertex Deletion can be solved in time 8 k · n O(1). The major obstacle to this end is how to handle a long induced cycle as an obstruction. To fix this issue, we define the necklace graphs and investigate their structural properties. We also show that the LRW1-Vertex Deletion has a polynomial kernel.en
dc.identifier.citationpages139-150en
dc.relation.ispartoftitleIPEC: International symposium on Parameterized and Exact Computationen
dc.relation.ispartofpublnameSchloss Dagstuhl--Leibniz-Zentrum fuer Informatiken
dc.identifier.urlsitehttps://hal-lirmm.ccsd.cnrs.fr/lirmm-01264011en
dc.subject.ddclabelPrincipes généraux des mathématiquesen
dc.relation.ispartofisbn978-3-95977-140-5en
dc.relation.conftitle10th International Symposium on Parameterized and Exact Computation (IPEC 2015)en
dc.relation.confdate2015-09
dc.relation.confcityPatrasen
dc.relation.confcountryGreeceen
dc.relation.forthcomingnonen
dc.identifier.doi10.4230/LIPIcs.IPEC.2015.138en
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2020-09-25T14:02:17Z
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