In the mathematical theory of matroids , a graphic matroid also called a cycle matroid or polygon matroid is a matroid whose independent sets are the forests in a given finite undirected graph. The dual matroids of graphic matroids are called co-graphic matroids or bond matroids. More generally, a matroid is called graphic whenever it is isomorphic to the graphic matroid of a graph, regardless of whether its elements are themselves edges in a graph. Since the lattices of flats of matroids are exactly the geometric lattices , this implies that the lattice of partitions is also geometric. Such a matrix has one row for each vertex, and one column for each edge.
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In this paper, we obtain a forbidden minor characterization of a cographic matroid M for which the splitting matroid M x,y is graphic for every pair x, y of elements of M. Borse, Forbidden-minors for splitting binary gammoids, Australas.
Borse, M. Shikare and K. Dalvi, Excluded-minors for the class of co- graphic splitting matroids, Ars Combin. Harary, Graph Theory Addison-Wesley, Mills, On the cocircuits of a splitting matroid, Ars Combin.
Raghunathan, M. Shikare and B. Waphare, Splitting in a binary matroid, Discrete Math. Shikare, Splitting lemma for binary matroids, Southeast Asian Bull.
Shikare and G. Azadi, Determination of the bases of a splitting matroid, European J. Waphare, Excluded-minors for the class of graphic splitting matroids, Ars Combin. Home About us Subject Areas Contacts. Advanced Search Help. Sciendo degruyter. Sign In Create Profile. English Deutsch. Naiyer Pirouz naiyer. Access Metrics. Keywords: binary matroid ; graphic matroid ; cographic matroid ; minor ; splitting operation. Discussiones Mathematicae Graph Theory. Terms Privacy Latest News.
Graphic and Cographic Г-Extensions of Binary Matroids
Graphic Splitting of Cographic Matroids