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Matroids having the same connectivity function

✍ Scribed by Manoel Lemos

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 532 KB
Volume: 131
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90380-8

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✦ Synopsis

We define the connectivity function of a matroid M on a set

E as c(M; X)=r(X)+r(E\X)-r(E)+

1(X c E), where r is the rank function of M. Cunningham conjectured that a connected matroid is determined, up to duality, by its connectivity function. proved this for binary matroids and we shall prove it in general provided

r(M)#r(M*).

Seymour in 1988 gave a counterexample for this conjecture.

or M,.

As a corollary of Theorem 1, we have the following result.

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