… We define a matroid M on a set M, its flats and their dimensions as in HI, ?1. We call the
dimension … separation of the flat SU Y of M is { S, Y} (HI, ?4). If such a separation exists we have …

… on the set of these separations: we do not need that they ‘separate’ anything, such as the
ground set of a matroid or the vertex set of a graph, … level of abstract separation systems [6]: we …

… On one hand, we were tempted to prove all matroid results … flows in matroids by borrowing
ideas from flows in graphs. A … vertex kseparation of G if and only if it is a cycle k-separation of G…

… Cut are two fundamental graph separation problems in algorithmic graph theory. We …
matroids. It is customary to begin the discussion on our framework with Vertex Cover (given a graph …

… A matroid is graphic if it is the polygon matroid of some graph.… , of M, and M, to be the matroid
on S, US, which has as circuits … same as having an exact 3-separation; indeed, we shall see …

… For a positive integer k, a k-separation of a matroid M is a partition {X, Y} of … matroid
concept that does generalize the graph notion [2, 4, 5]. For a positive integer k, a vertical k-separation …

… ^-separation is more restrictive. In this section we shall relate the notions of ^-connection for
graphs and … We take M to be an arbitrary matroid on a set E. From (7) and (8) we deduce that …

… As a corollary of the result on k-separations with k ≤ 2, we … that the graph G obtain from
identifying a vertex in a graph G … invariant on the class of graphs that have the same cycle matroid…

… S,’ be 3 distinct cocircuits of a matroid M on a set E. We say that S,’ does not separate SI’ and
S,’ … Our main result is: A matroid is graphic if and only if from any 3 cocircuits having a non-…

… For the second class, we show that an undirected graph G gives rise to a pure oriented matroid
if … Next, we give some technical background on zonotopal tilings and oriented matroids in …