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On matroid connectivity

✍ Scribed by James Oxley; Haidong Wu

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
138 KB
Volume
146
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

✦ Synopsis

If M is a loopless matroid in which MIX and MI Y are connected and X c~ Y is non-empty, then one easily shows that MI(X u Y) is connected. Likewise, it is straightforward to show that if G and H are n-connected graphs having at least n common vertices, then G u H is nconnected. The purpose of this note is to prove a matroid connectivity result that is a common generalization of these two observations.

πŸ“œ SIMILAR VOLUMES

Theorems on matroid connectivity
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A 3-separation (A, B), in a matroid M, is called sequential if the elements of A can be ordered (a 1 , ..., a k ) such that, for i=3, ..., k, ([a 1 , ..., a i ], [a i+1 , ..., a k ] \_ B) is a 3-separation. A matroid M is sequentially 4-connected if M is 3-connected and, for every 3-separation (A, B