{"@context":"https:\/\/schema.org\/","@type":"ScholarlyArticle","@id":"#article7652","name":"Connecting Vertices by Independent Trees","abstract":"We study the paramereteized complexity of the following connectivity problem. For a vertex subset U of a graph G, trees T_1,...,T_s of G are completely independent spanning trees of U if each of them contains U, and for every two distinct vertices u,v in U, the paths from u to v in T_1,...,T_s are pairwise vertex disjoint except for end-vertices u and v. Then for a given s >= 2 and a parameter k, the task is to decide if a given n-vertex graph G contains a set U of size at least k such that there are s completely independent spanning trees of U. The problem is known to be NP-complete already for s=2. We prove the following results: (*) For s=2 the problem is solvable in time 2^{O(k)}*n^{O(1)}. (*) For s=2 the problem does not admit a polynomial kernel unless NP subseteq coNP\/poly. (*) For arbitrary s, we show that the problem is solvable in time f(s,k)n^{O(1)} for some function f of s and k only.","keywords":["Parameterized complexity","FPT-algorithms","completely independent spanning trees"],"author":[{"@type":"Person","name":"Basavaraju, Manu","givenName":"Manu","familyName":"Basavaraju"},{"@type":"Person","name":"Fomin, Fedor V.","givenName":"Fedor V.","familyName":"Fomin"},{"@type":"Person","name":"Golovach, Petr A.","givenName":"Petr A.","familyName":"Golovach"},{"@type":"Person","name":"Saurabh, Saket","givenName":"Saket","familyName":"Saurabh"}],"position":8,"pageStart":73,"pageEnd":84,"dateCreated":"2014-12-12","datePublished":"2014-12-12","isAccessibleForFree":true,"license":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/legalcode","copyrightHolder":[{"@type":"Person","name":"Basavaraju, Manu","givenName":"Manu","familyName":"Basavaraju"},{"@type":"Person","name":"Fomin, Fedor V.","givenName":"Fedor V.","familyName":"Fomin"},{"@type":"Person","name":"Golovach, Petr A.","givenName":"Petr A.","familyName":"Golovach"},{"@type":"Person","name":"Saurabh, Saket","givenName":"Saket","familyName":"Saurabh"}],"copyrightYear":"2014","accessMode":"textual","accessModeSufficient":"textual","creativeWorkStatus":"Published","inLanguage":"en-US","sameAs":"https:\/\/doi.org\/10.4230\/LIPIcs.FSTTCS.2014.73","publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","isPartOf":{"@type":"PublicationVolume","@id":"#volume6232","volumeNumber":29,"name":"34th International Conference on Foundation of Software Technology and Theoretical Computer Science (FSTTCS 2014)","dateCreated":"2014-12-12","datePublished":"2014-12-12","editor":[{"@type":"Person","name":"Raman, Venkatesh","givenName":"Venkatesh","familyName":"Raman"},{"@type":"Person","name":"Suresh, S. P.","givenName":"S. P.","familyName":"Suresh"}],"isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#article7652","isPartOf":{"@type":"Periodical","@id":"#series116","name":"Leibniz International Proceedings in Informatics","issn":"1868-8969","isAccessibleForFree":true,"publisher":"Schloss Dagstuhl \u2013 Leibniz-Zentrum f\u00fcr Informatik","hasPart":"#volume6232"}}}