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2007

The structure of 3-connected matroids of path width three

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The structure of 3-connected matroids of path width three
A 3-connected matroid M is sequential or has path width 3 if its ground set E(M) has a sequential ordering, that is, an ordering (e1, e2, . . . , en) such that ({e1, e2, . . . , ek}, {ek+1, ek+2, . . . , en}) is a 3-separation for all k in {3, 4, . . . , n − 3}. In this paper, we consider the possible sequential orderings that such a matroid can have. In particular, we prove that M essentially has two fixed ends, each of which is a maximal segment, a maximal cosegment, or a maximal fan. We also identify the possible structures in M that account for different sequential orderings of E(M). These results rely on an earlier paper of the authors that describes the structure of equivalent non-sequential 3-separations in a 3-connected matroid. Those results are extended here to describe the structure of equivalent sequential 3-separations.
Rhiannon Hall, James G. Oxley, Charles Semple
Added 13 Dec 2010
Updated 13 Dec 2010
Type Journal
Year 2007
Where EJC
Authors Rhiannon Hall, James G. Oxley, Charles Semple
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