منابع مشابه
Adjacency, Inseparability, and Base Orderability in Matroids
Two elements in an oriented matroid are inseparable if they have either the same sign in every signed circuit containing them both or opposite signs in every signed circuit containing them both. Two elements of a matroid are adjacent if there is no M(K4)-minor using them both, and in which they correspond to a matching of K4. We prove that two elements e, { of an oriented matroid are inseparabl...
متن کاملAn Adjacency Criterion for Coxeter Matroids
A coxeter matroid is a generalization of matroid, ordinary matroid being the case corresponding to the family of Coxeter groups An , which are isomorphic to the symmetric groups. A basic result in the subject is a geometric characterization of Coxeter matroid in terms of the matroid polytope, a result first stated by Gelfand and Serganova. This paper concerns properties of the matroid polytope....
متن کاملRemovable Circuits in Binary Matroids
We show that if M is a connected binary matroid of cogirth at least ve which does not have both an F 7-minor and an F 7-minor, then M has a circuit C such that M ? C is connected and r(M ? C) = r(M).
متن کاملA construction for binary matroids
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. Its circuits are the minimal members of this collection. We use this basic property to derive binary matroids from binary matroids. In particular, we derive two matroids from graphic and cographic matroids. Cocycles of the first one are cutsets or balancing...
متن کاملInvolutions Of Connected Binary Matroids
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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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 1986
ISSN: 0195-6698
DOI: 10.1016/s0195-6698(86)80043-9