Results 121 to 130 of about 4,003 (147)

Removable Circuits in Binary Matroids

Combinatorics, Probability and Computing, 1999
We show that, if M is a connected binary matroid of cogirth at least five which does not have both an F7-minor and an F*7-minor, then M has a circuit C such that M − C is connected and r(M − C) = r(M).
Goddyn, Luis A., Jackson, Bill
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On Minimally 3-Connected Binary Matroids

Combinatorics, Probability and Computing, 2001
We generalize a minimal 3-connectivity result of Halin from graphs to binary matroids. As applications of this theorem to minimally 3-connected matroids, we obtain new results and short inductive proofs of results of Oxley and Wu. We also give new short inductive proofs of results of Dirac and Halin on minimally k-connected graphs for k ∈ {2,3}.
Reid, Talmage James, Wu, Haidong
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Involutions of Connected Binary Matroids

Combinatorics, Probability and Computing, 2000
We prove that if an involution ϕ is an automorphism of a connected binary matroid M then there is a hyperplane of M that is invariant under ϕ. We also consider extensions of this result for higher connectivity.
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Decomposition of binary matroids

Combinatorica, 1985
The first part studies balanced sets in a matroid: If a matroid on E with rank function \(\rho\) is induced by an integer polymatroid \(\mu\) (as a submodular set function) then \(A\subseteq E\) is \(\mu\)-balanced if \(\mu A=\rho A_ iA\) is balanced if it is \(\mu\)-balanced for every such \(\mu\). This concept was introduced by the author in J. Math.
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Biased graphs whose matroids are special binary matroids

Graphs and Combinatorics, 1990
A biased graph \(\Omega\) is a graph \(\Gamma\) together with a class \({\mathcal B}\) of polygons of \(\Gamma\) such that no theta-subgraph of \(\Gamma\) contains exactly two members of \({\mathcal B}\). (Examples arise form signed graphs by letting \({\mathcal B}\) consist of the polygons with an even number of minus-signs.) A subgraph \(S\) is ...
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Gröbner Representations of Binary Matroids

2009
Several constructions in binary linear block codes are also related to matroid theory topics. These constructions rely on a given order in the ground set of the matroid. In this paper we define the Grobner representation of a binary matroid and we show how it can be used for studying different sets bases, cycles, activity intervals, etc.
M. Borges-Quintana, M. A. Borges-Trenard, E. Martínez-Moro   +2 more
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Symmetric Representations of Binary Matroids

1983
To every symmetric matrix A with coefficients in GF(2) is associated on the one hand the binary matroid M(A ) (matroid of the linear independence of columns, of which A is a representation), and on the other hand the simple graph G(A ), the vertex-to-vertex adjacency matrix of which has the same non-diagonal elements as A .
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BINARY MATROID SUMS

The Quarterly Journal of Mathematics, 1979
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Recognizing even-cycle and even-cut matroids

Mathematical Programming, 2023
Bertrand Guenin
exaly  

Rainbow and monochromatic circuits and cocircuits in binary matroids

Discrete Mathematics, 2022
Kristóf Bérczi, Tamás Schwarcz
exaly