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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/24968

Title: Isotropic matroids III: Connectivity
Authors: Brijder, Robert
Traldi, Lorenzo
Issue Date: 2017
Citation: 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.
URI: http://hdl.handle.net/1942/24968
Link to publication: http://www.combinatorics.org/ojs/index.php/eljc/article/view/v24i2p49/pdf
ISI #: 000408657300007
ISSN: 1077-8926
Category: A1
Type: Journal Contribution
Appears in Collections: Research publications

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