Oriented matroids and combinatorial manifolds

January 1993

The paper discusses connectivity properties of graphs of combinatorial manifolds (abstract polytopes) which are related to oriented matroids. By a result of Barnette, the graph of a $d$-manifold is\break $(d+1)$-connected. The lattice of faces of an acyclic oriented matroid of rank $r$ is an $(r-2)$-manifold, and hence its graph and the graph of its polar (dual) are $(r-1)$-connected. An oriented matroid lattice is a lattice arising from the span of cocircuits of an oriented matroid ordered by conformal relation. If the rank of the oriented matroid is $r$, this is an $(r-1)$-manifold and hence its graph $G$ and the graph of its polar are $r$-connected. However, the authors prove that $G$ is indeed $(2r-2)$-connected. Reviewed by E.Schulte

Authors in the community:

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  R

  Raúl Manuel Cordovil Cordeiro Vinagre

  ist23593

European Journal of Combinatorics

9

15

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mathematics - Mathematics

eng - English