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oai:drops-oai.dagstuhl.de:6274 2024-03-06T10:37:38Z ddc:004 open_access

Quasi-4-Connected Components Grohe, Martin decompositions connectivity tangles We introduce a new decomposition of a graphs into quasi-4-connected components, where we call a graph quasi-4-connected if it is 3-connected and it only has separations of order 3 that separate a single vertex from the rest of the graph. Moreover, we give a cubic time algorithm computing the decomposition of a given graph. Our decomposition into quasi-4-connected components refines the well-known decompositions of graphs into biconnected and triconnected components. We relate our decomposition to Robertson and Seymour's theory of tangles by establishing a correspondence between the quasi-4-connected components of a graph and its tangles of order 4. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Martin Grohe 2016 Is Part Of LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2016.8 urn:nbn:de:0030-drops-62740 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.8 eng https://creativecommons.org/licenses/by/3.0/legalcode