Results 71 to 80 of about 4,000 (161)
A construction for binary matroids
Discrete Mathematics, 1987 A family of subsets of a ground set closed under the operation of taking symmetric differences is the family of cycles of a binary matroid, whose circuits are the minimal members of this collection. Using this fact two binary matroids are derived from graphic and ergodic matroids. Cocycles of the first one are cutsets or balancing sets. Cocycles of the
Barahona, F., CONFORTI, MICHELANGELO
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Turán's Triangle Theorem and Binary Matroids
European Journal of Combinatorics, 1989 A special case of a theorem of Turán is that a graph on v vertices, with no loops, parallel edges, or triangles, has no more than \(\lfloor v/2\rfloor \lceil v/2\rceil\) edges. This bound is achieved by a graph G if and only if \(G\cong K_{\lfloor v/2\rfloor,\lceil v/2\rceil}\). We generalize this result to binary maroids.
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Connected hyperplanes in binary matroids
Linear Algebra and its Applications, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lemos, Manoel, Melo, T.R.B.
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On Binary Identically Self-dual Matroids
European Journal of Combinatorics, 1984 A matroid is identically self-dual when its set of bases is identical with its set of co-bases. The author proves that the only connected regular identically self-dual matroid is the uniform matroid of rank 1 on two points. He improves the known lower bound for the number of bases in an identically self-dual matroid.
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Γ-Extension of Binary Matroids [PDF]
ISRN Discrete Mathematics, 2011 We extend the notion of a point-addition operation from graphs to binary matroids. This operation can be expressed in terms of element-addition operation and splitting operation. We consider a special case of this construction and study its properties. We call the resulting matroid of this special case a Γ-extension of the given matroid.
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Binary Matroids with Graphic Cocircuits
, 2012 An excluded minor characterization for the class of binary signed-graphic matroids with graphic cocircuits is provided. In this report we present the necessary computations for the case analysis in the proof.
Papalamprou, Konstantinos +1 more
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Approximation operators via TD-matroids on two sets. [PDF]
Soft comput, 2022 Wang G, Mao H.
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On k-Connected Γ-Extensions of Binary Matroids
Lobachevskii Journal of Mathematics, 2018 Slater introduced the point-addition operation on graphs to classify 4-connected graphs. The $ $-extension operation on binary matroids is a generalization of the point-addition operation. In this paper, we obtain necessary and sufficient conditions to preserve $k$-connectedness of a binary matroid under the $ $-extension operation.
Borse, Y. M., Mundhe, Ganesh
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Rough set approximations based on a matroidal structure over three sets. [PDF]
Appl Intell (Dordr), 2023 Wang G, Mao H, Liu C, Zhang Z, Yang L.
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The Smallest Rounded Sets of Binary Matroids
European Journal of Combinatorics, 1990 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Oxley, James G., Reid, Talmage James
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