Results 21 to 30 of about 155 (58)
The excluded minors for 2- and 3-regular matroids
, 2023 The class of 2-regular matroids is a natural generalisation of regular and near-regular matroids. We prove an excluded-minor characterisation for the class of 2-regular matroids.
Brettell, Nick +3 more
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Excluding Kuratowski graphs and their duals from binary matroids
, 2017 We consider some applications of our characterisation of the internally 4-connected binary matroids with no M(K3,3)-minor. We characterise the internally 4-connected binary matroids with no minor in some subset of {M(K3,3),M*(K3,3),M(K5),M*(K5)} that ...
Mayhew, Dillon +2 more
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Matroids in which every pair of elements belongs to both a 4-circuit and a 4-cocircuit
, 2014 In this thesis, we analyse the matroids which have the property that every pair of elements belongs to both a 4-circuit and a 4-cocircuit. In particular, we show that if a matroid with this property has at least 13 elements, then it is a spike.
Miller, Joel
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Characterizing binary matroids with no P9-minor [PDF]
, 2015 In this paper, we give a complete characterization of binary matroids with no P9-minor. A 3-connected binary matroid M has no P9-minor if and only if M is a 3-connected regular matroid, a binary spike with rank at least four, one of the internally 4 ...
Ding, Guoli, Wu, Haidong
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A characterization of graphic matroids using non-separating cocircuits
Advances in Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +1 more source
Fan-extensions in fragile matroids [PDF]
, 2015 If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of ...
Chun, Carolyn +3 more
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Towards a splitter theorem for internally 4-connected binary matroids VI [PDF]
, 2018 Let M be a 3-connected binary matroid; M is called internally 4-connected if one side of every 3-separation is a triangle or a triad, and M is internally 4-connected if one side of every 3-separation is a triangle, a triad, or a 4-element fan.
Chun, Carolyn, Oxley, James
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Infinite Matroids and Determinacy of Games [PDF]
, 2013 Solving a problem of Diestel and Pott, we construct a large class of infinite matroids. These can be used to provide counterexamples against the natural extension of the Well-quasi-ordering-Conjecture to infinite matroids and to show that the class of ...
Bowler, Nathan, Carmesin, Johannes
core
On a generalisation of spikes [PDF]
, 2018 We consider matroids with the property that every subset of the ground set of size $t$ is contained in both an $\ell$-element circuit and an $\ell$-element cocircuit; we say that such a matroid has the $(t,\ell)$-property.
Brettell, Nick +4 more
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The Complexity of Order Type Isomorphism
, 2013 The order type of a point set in $R^d$ maps each $(d{+}1)$-tuple of points to its orientation (e.g., clockwise or counterclockwise in $R^2$). Two point sets $X$ and $Y$ have the same order type if there exists a mapping $f$ from $X$ to $Y$ for which ...
Aloupis, Greg +4 more
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