منابع مشابه
Isotropic Matroids III: Connectivity
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,...
متن کاملIsotropic Matroids II: Circle Graphs
We present several characterizations of circle graphs, which follow from Bouchet’s circle graph obstructions theorem.
متن کاملConnectivity Properties of Matroids
The bases-exchange graph of a matroid is the graph whose vertices are the bases of the matroid, and two bases are connected by an edge if and only if one can be obtained from the other by the exchange of a single pair of elements. In this paper we prove that a matroid is \connected" if and only if the \restricted bases-exchange graph" (the bases-exchange graph restricted to exchanges involving ...
متن کاملConnectivity in frame matroids
We discuss the relationship between the vertical connectivity of a biased graph Ω and the Tutte connectivity of the frame matroid of Ω (also known as the bias matroid of Ω).
متن کاملIsotropic Matroids I: Multimatroids and Neighborhoods
Several properties of the isotropic matroid of a looped simple graph are presented. Results include a characterization of the multimatroids that are associated with isotropic matroids and several ways in which the isotropic matroid of G incorporates information about graphs locally equivalent to G. Specific results of the latter type include a characterization of graphs that are locally equival...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2017
ISSN: 1077-8926
DOI: 10.37236/5937