DC Field | Value | Language |
---|---|---|

dc.contributor.author | Jeong, Jisu | ko |

dc.contributor.author | Kwon, O-Joung | ko |

dc.contributor.author | Oum, Sang-il | ko |

dc.date.accessioned | 2014-09-04T08:24:18Z | - |

dc.date.available | 2014-09-04T08:24:18Z | - |

dc.date.created | 2014-08-04 | - |

dc.date.created | 2014-08-04 | - |

dc.date.issued | 2014-10 | - |

dc.identifier.citation | EUROPEAN JOURNAL OF COMBINATORICS, v.41, pp.242 - 257 | - |

dc.identifier.issn | 0195-6698 | - |

dc.identifier.uri | http://hdl.handle.net/10203/189963 | - |

dc.description.abstract | Linear rank-width is a graph width parameter, which is a variation of rank-width by restricting its tree to a caterpillar. As a corollary of known theorems, for each k, there is a finite obstruction set O-k of graphs such that a graph G has linear rank-width at most k if and only if no vertex-minor of G is isomorphic to a graph in O-k However, no attempts have been made to bound the number of graphs in O-k for k >= 2. We show that for each k, there are at least 2(Omega(3k)) pairwise locally non-equivalent graphs in O-k, and therefore the number of graphs in O-k is at least double exponential. To prove this theorem, it is necessary to characterize when two graphs in O-k are locally equivalent. A graph is a block graph if all of its blocks are complete graphs. We prove that if two block graphs without simplicial vertices of degree at least 2 are locally equivalent, then they are isomorphic. This not only is useful for our theorem but also implies a theorem of Bouchet (1988) stating that if two trees are locally equivalent, then they are isomorphic. | - |

dc.language | English | - |

dc.publisher | ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD | - |

dc.subject | BRANCH-WIDTH | - |

dc.subject | OBSTRUCTIONS | - |

dc.title | Excluded vertex-minors for graphs of linear rank-width at most k | - |

dc.type | Article | - |

dc.identifier.wosid | 000338399000017 | - |

dc.identifier.scopusid | 2-s2.0-84900810518 | - |

dc.type.rims | ART | - |

dc.citation.volume | 41 | - |

dc.citation.beginningpage | 242 | - |

dc.citation.endingpage | 257 | - |

dc.citation.publicationname | EUROPEAN JOURNAL OF COMBINATORICS | - |

dc.identifier.doi | 10.1016/j.ejc.2014.04.010 | - |

dc.contributor.localauthor | Oum, Sang-il | - |

dc.type.journalArticle | Article | - |

dc.subject.keywordPlus | BRANCH-WIDTH | - |

dc.subject.keywordPlus | OBSTRUCTIONS | - |

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