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DC Field | Value | Language |
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dc.contributor.author | BRIJDER, Robert | - |
dc.contributor.author | Hoogeboom, Hendrik Jan | - |
dc.contributor.author | Traldi, Lorenzo | - |
dc.date.accessioned | 2013-09-20T10:44:29Z | - |
dc.date.available | 2013-09-20T10:44:29Z | - |
dc.date.issued | 2013 | - |
dc.identifier.citation | ELECTRONIC JOURNAL OF COMBINATORICS, 20 (3) | - |
dc.identifier.issn | 1077-8926 | - |
dc.identifier.uri | http://hdl.handle.net/1942/15500 | - |
dc.description.abstract | If G is a looped graph, then its adjacency matrix represents a binary matroid MA(G) on V (G). MA(G) may be obtained from the delta-matroid represented by the adjacency matrix of G, but MA(G) is less sensitive to the structure of G. Jaeger proved that every binary matroid is MA(G) for some G [Ann. Discrete Math. 17 (1983), 371-376]. The relationship between the matroidal structure of MA(G) and the graphical structure of G has many interesting features. For instance, the matroid minors MA(G) − v and MA(G)/v are both of the form MA(G′ − v) where G′ may be obtained from G using local complementation. In addition, matroidal considerations lead to a principal vertex tripartition, distinct from the principal edge tripartition of Rosenstiehl and Read [Ann. Discrete Math. 3 (1978), 195-226]. Several of these results are given two very different proofs, the first involving linear algebra and the second involving set systems or -matroids. Also, the Tutte polynomials of the adjacency matroids of G and its full subgraphs are closely connected to the interlace polynomial of Arratia, Bollob´as and Sorkin [Combinatorica 24 (2004), 567-584]. | - |
dc.language.iso | en | - |
dc.subject.other | adjacency; delta-matroid; interlace polynomial; local complement; matroid; minor; Tutte polynomial | - |
dc.title | The adjacency matroid of a graph | - |
dc.type | Journal Contribution | - |
dc.identifier.issue | 3 | - |
dc.identifier.volume | 20 | - |
local.format.pages | 38 | - |
local.bibliographicCitation.jcat | A1 | - |
dc.description.notes | Brijder, R (reprint author), Hasselt Univ, Diepenbeek, Belgium. robert.brijder@uhasselt.be; h.j.hoogeboom@cs.leidenuniv.nl; traldil@lafayette.edu | - |
local.type.refereed | Refereed | - |
local.type.specified | Article | - |
dc.identifier.isi | 000323793600002 | - |
dc.identifier.url | http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i3p27 | - |
item.fullcitation | BRIJDER, Robert; Hoogeboom, Hendrik Jan & Traldi, Lorenzo (2013) The adjacency matroid of a graph. In: ELECTRONIC JOURNAL OF COMBINATORICS, 20 (3). | - |
item.fulltext | With Fulltext | - |
item.validation | ecoom 2014 | - |
item.contributor | BRIJDER, Robert | - |
item.contributor | Hoogeboom, Hendrik Jan | - |
item.contributor | Traldi, Lorenzo | - |
item.accessRights | Open Access | - |
crisitem.journal.issn | 1077-8926 | - |
crisitem.journal.eissn | 1077-8926 | - |
Appears in Collections: | Research publications |
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File | Description | Size | Format | |
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1107.5493v6.pdf | 398.04 kB | Adobe PDF | View/Open |
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