DC Field | Value | Language |
---|---|---|
dc.contributor.author | DeVos, Matt | ko |
dc.contributor.author | Kwon, O-joung | ko |
dc.contributor.author | Oum, Sang-il | ko |
dc.date.accessioned | 2020-09-28T02:55:10Z | - |
dc.date.available | 2020-09-28T02:55:10Z | - |
dc.date.created | 2020-09-23 | - |
dc.date.issued | 2020-12 | - |
dc.identifier.citation | EUROPEAN JOURNAL OF COMBINATORICS, v.90 | - |
dc.identifier.issn | 0195-6698 | - |
dc.identifier.uri | http://hdl.handle.net/10203/276402 | - |
dc.description.abstract | We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns closely with the notions of tree-depth and shrub-depth of graphs as follows. For a graph G = (V, E) and a subset A of E we let lambda(G)(A) be the number of vertices incident with an edge in A and an edge in E \ A. For a subset X of V, let rho(G)(X) be the rank of the adjacency matrix between X and V \ X over the binary field. We prove that a class of graphs has bounded tree-depth if and only if the corresponding class of functions lambda(G) has bounded branch depth and similarly a class of graphs has bounded shrub-depth if and only if the corresponding class of functions rho(G) has bounded branch-depth, which we call the rank-depth of graphs. Furthermore we investigate various potential generalizations of tree-depth to matroids and prove that matroids representable over a fixed finite field having no large circuits are well-quasi ordered by restriction. | - |
dc.language | English | - |
dc.publisher | ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD | - |
dc.title | Branch-depth: Generalizing tree-depth of graphs | - |
dc.type | Article | - |
dc.identifier.wosid | 000565160300001 | - |
dc.identifier.scopusid | 2-s2.0-85087922057 | - |
dc.type.rims | ART | - |
dc.citation.volume | 90 | - |
dc.citation.publicationname | EUROPEAN JOURNAL OF COMBINATORICS | - |
dc.identifier.doi | 10.1016/j.ejc.2020.103186 | - |
dc.contributor.localauthor | Oum, Sang-il | - |
dc.contributor.nonIdAuthor | DeVos, Matt | - |
dc.contributor.nonIdAuthor | Kwon, O-joung | - |
dc.description.isOpenAccess | Y | - |
dc.type.journalArticle | Article | - |
dc.subject.keywordPlus | MONADIC 2ND-ORDER LOGIC | - |
dc.subject.keywordPlus | RANK-WIDTH | - |
dc.subject.keywordPlus | MINORS | - |
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