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A note on roundedness in 4-connected matroids

✍ Scribed by Talmage James Reid

Publisher: Elsevier Science
Year: 1991
Tongue: English
Weight: 237 KB
Volume: 91
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(91)90113-g

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✦ Synopsis

A k-connected matroid M with at least four elements is (k,2)-rounded if it satisfies the following condition. Whenever e and f are elements of a k-connected matroid N having M as a minor, then N has a minor which uses e and f and is isomorphic to M. We show that, for k exceeding three, a (k, 2)-rounded matroid must have rank or corank less than k. The corresponding result for k = 3 was proved by Oxley. As a consequence, we show that M is (4,2)-rounded if and only if M is isomorphic to U,,,. This extends results of Coullard, Kahn, and Oxley.

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