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http://hdl.handle.net/1942/24968
Title: | Isotropic matroids III: Connectivity | Authors: | BRIJDER, Robert Traldi, Lorenzo |
Issue Date: | 2017 | Publisher: | ELECTRONIC JOURNAL OF COMBINATORICS | Source: | ELECTRONIC JOURNAL OF COMBINATORICS, 24(2), p. 1-25 (Art N° P2.49) | Abstract: | The isotropic matroid M[IAS(G)] of a graph G is a binary matroid, which is equivalent to the isotropic system introduced by Bouchet. In this paper we discuss four notions of connectivity related to isotropic matroids and isotropic systems. We show that the isotropic system connectivity defined by Bouchet is equivalent to vertical connectivity of M[IAS(G)], and if G has at least four vertices, then M[IAS(G)] is vertically 5-connected if and only if G is prime (in the sense of Cunningham's split decomposition). We also show that MIAS(G)] is 3-connected if and only if G is connected and has neither a pendant vertex nor a pair of twin vertices. Our most interesting theorem is that if G has n >= 7 vertices then M[IAS(G)] is not vertically n-connected. This abstract-seeming result is equivalent to the more concrete assertion that G is locally equivalent to a graph with a vertex of degree < n-1/2. | Notes: | [Brijder, Robert] Hasselt Univ, Hasselt, Belgium. [Traldi, Lorenzo] Lafayette Coll, Easton, PA 18042 USA. | Keywords: | circle graph; connectivity; degree; isotropic system; local equivalence; matroid; pendant; prime; split; twin;circle graph; connectivity; degree; isotropic system; local equivalence; matroid; pendant; prime; split; twin | Document URI: | http://hdl.handle.net/1942/24968 | Link to publication/dataset: | http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p49/pdf | ISSN: | 1077-8926 | e-ISSN: | 1077-8926 | ISI #: | 000408657300007 | Rights: | the electronic journal of combinatorics | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2018 |
Appears in Collections: | Research publications |
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isotropc.pdf | Published version | 415.21 kB | Adobe PDF | View/Open |
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