A graph-theoretical axiomatization of oriented matroids
نویسندگان
چکیده
We characterize which systems of sign vectors are the cocircuits of an oriented matroid in terms of the cocircuit graph.
منابع مشابه
Generation of Oriented Matroids - A Graph Theoretical Approach
We discuss methods for the generation of oriented matroids and of isomorphism classes of oriented matroids. Our methods are based on single element extensions and graph theoretical representations of oriented matroids, and all these methods work in general rank and for nonuniform and uniform oriented matroids as well. We consider two types of graphs, cocircuit graphs and tope graphs, and discus...
متن کاملAn Elementary Approach to Symplectic Matroids
Newcomers to the theory of Coxeter matroids are often frustrated by the complexity of the basic de nitions. The main result of this paper is an independent set axiomatization of symplectic matroids, a large and important class of Coxeter matroids. This axiomatization provides the most elementary de nition of symplectic matroids to date. Our hope is that it will make the subject much more access...
متن کاملOn tope graphs of complexes of oriented matroids
We give two graph theoretical characterizations of tope graphs of (complexes of) oriented matroids. The first is in terms of excluded partial cube minors, the second is that all antipodal subgraphs are gated. A direct consequence is a third characterization in terms of zone graphs of tope graphs. Further corollaries include a characterization of topes of oriented matroids due to da Silva, anoth...
متن کاملStructural properties of fuzzy graphs
Matroids are important combinatorial structures and connect close-lywith graphs. Matroids and graphs were all generalized to fuzzysetting respectively. This paper tries to study connections betweenfuzzy matroids and fuzzy graphs. For a given fuzzy graph, we firstinduce a sequence of matroids from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. A fuzzy matroid, named graph fuzzy matro...
متن کاملA Universal Axiomatization of Metropolis-rota Implication Algebras
We show that the class of Metropolis-Rota implication algebras can be given a universal axiomatization using an operation closely related to composition in oriented matroids. Lastly we describe the role of our new operation in the collapse of an MRalgebra.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Eur. J. Comb.
دوره 35 شماره
صفحات -
تاریخ انتشار 2011