17 graph. The cuts of G are the minimal dependent sets of a matroid T ? (G) on the edge set E. A matroid T is cographic if there exists some graph G such that T is isomorphic to the cut matroid T ? (G). Every cographic matroid is representable over any eld 18]. Therefore if an access structure A has a cographic appropriate matroid, then A is universally ideal. Unlike graphic matroids, we do not...

We prove that the ranks of the subsets and the activities of the bases of a matroid define valuations for the subdivisions of a matroid polytope into smaller matroid polytopes.

Given an undirected graph G = (V,E) and a delta-matroid (V,F), the delta-matroid matching problem is to find a maximum cardinality matching M such that the set of the end vertices of M belongs to F . This problem is a natural generalization of the matroid matching problem to delta-matroids, and thus it cannot be solved in polynomial time in general. This paper introduces a class of the delta-ma...

The main purpose of this study is to discuss the uniform boundednessprinciple in fuzzifying topological linear spaces. At first theconcepts of uniformly boundedness principle and fuzzy equicontinuousfamily of linear operators are proposed, then the relations betweenfuzzy equicontinuous and uniformly bounded are studied, and with thehelp of net convergence, the characterization of fuzzyequiconti...

Since Chang [2] introduced fuzzy theory into topology, many authors have discussed various aspects of fuzzy topology. It is well known that weakly induced and induced topological spaces play an important role in L-topological spaces (see book [8]). According to their value ranges, L-topological spaces form different categories. Clearly, the investigation on their relationships is certainly impo...

AND GENERIC RIGIDITY IN THE PLANE SACHIN PATKAR, BRIGITTE SERVATIUS, AND K. V. SUBRAHMANYAM Abstract. We consider the concept of abstract 2–dimensional rigidity and provide necessary and sufficient conditions for a matroid to be an abstract rigidity matroid of a complete graph. This characterization is a natural extenWe consider the concept of abstract 2–dimensional rigidity and provide necessa...

The matroid parity (MP) problem is a natural extension of the matching problem to the matroid setting. It can be formulated as a 0− 1 linear program using the so-called rank and line constraints. We call the associated family of polytopes MP polytopes. We then prove the following: (i) when the matroid is a gammoid, each MP polytope is a projection of a perfect matching polytope into a suitable ...