Library

X
feed icon rss

Your email was sent successfully. Check your inbox.

An error occurred while sending the email. Please try again.

Proceed reservation?

Export
Filter
  • 1
    Electronic Resource
    Electronic Resource
    On the Cocircuit Graph of an Oriented Matroid (2000)
    Springer
    Discrete & computational geometry 24 (2000), S. 257-266 
    Details
    ISSN: 1432-0444
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract. In this paper we consider the cocircuit graph G M of an oriented matroid M , the 1 -skeleton of the cell complex W formed by the span of the cocircuits of M . In general, W is not determined by G M . However, we show that if the vertex set (resp. edge set) of G M is properly labeled by the hyperplanes (resp. colines) of M , G M determines W . Also we prove that, when M is uniform, the cocircuit graph together with all antipodal pairs of vertices being marked determines W . These results can be considered as variations of Blind—Mani's theorem that says the 1-skeleton of a simple convex polytope determines its face lattice.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004540010031
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
  • 2
    Electronic Resource
    Electronic Resource
    Bases-cobases graphs and polytopes of matroids (1993)
    Springer
    Combinatorica 13 (1993), S. 157-165 
    Details
    ISSN: 1439-6912
    Keywords: 05 B 35 ; 05 C 38
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract LetM be ablock matroid (i.e. a matroid whose ground setE is the disjoint union of two bases). We associate withM two objects: 1. Thebases-cobases graph G=G(M,M *) having as vertices the basesB ofM for which the complementE\B is also a base, and as edges the unordered pairs (B,B′) of such bases differing exactly by two elements. 2. Thepolytope of the bases-cobases K=K(M,M *) whose extreme points are the incidence vectors of the bases ofM whose complement is also a base. We prove that, ifM is graphic (or cographic), the distance between any two vertices ofG corresponding to disjoint bases is equal to the rank ofM (generalizing a result of [10]). Concerning the polytope we prove thatK is an hypercube if and only if dim(K)=rank(M). A constructive characterization of the class of matroids realizing this equality is given.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01303201
    Library Location Call Number Volume/Issue/Year Availability
    BibTip Others were also interested in ...
    Paper (German National Licenses)
    Fulltext
Close ⊗
This website uses cookies and the analysis tool Matomo. More information can be found here...