Full metadata record
DC Field | Value | Language |
---|---|---|
dc.contributor.author | 권오정 | - |
dc.date.accessioned | 2022-09-22T01:56:16Z | - |
dc.date.available | 2022-09-22T01:56:16Z | - |
dc.date.issued | 2020-12 | - |
dc.identifier.citation | EUROPEAN JOURNAL OF COMBINATORICS, v. 90, article no. 103186 | en_US |
dc.identifier.issn | 0195-6698; 1095-9971 | en_US |
dc.identifier.uri | https://www.sciencedirect.com/science/article/pii/S0195669820301074?via%3Dihub | en_US |
dc.identifier.uri | https://repository.hanyang.ac.kr/handle/20.500.11754/173188 | - |
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. | en_US |
dc.description.sponsorship | Supported by an NSERC Discovery Grant (Canada). Supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Education (No. NRF-2018R1D1A1B07050294). Supported by the Institute for Basic Science (IBS-R029-C1). | en_US |
dc.language.iso | en | en_US |
dc.publisher | ACADEMIC PRESS LTD- ELSEVIER SCIENCE LTD | en_US |
dc.title | Branch-depth: Generalizing tree-depth of graphs | en_US |
dc.type | Article | en_US |
dc.identifier.doi | 10.1016/j.ejc.2020.103186 | en_US |
dc.relation.journal | EUROPEAN JOURNAL OF COMBINATORICS | - |
dc.contributor.googleauthor | DeVos, Matt | - |
dc.contributor.googleauthor | Kwon, O-joung | - |
dc.contributor.googleauthor | Oum, Sang-il | - |
dc.relation.code | 2020050757 | - |
dc.sector.campus | S | - |
dc.sector.daehak | COLLEGE OF NATURAL SCIENCES[S] | - |
dc.sector.department | DEPARTMENT OF MATHEMATICS | - |
dc.identifier.pid | ojoungkwon | - |
dc.identifier.orcid | https://orcid.org/0000-0003-1820-1962 | - |
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