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 n
โฆ LIBER โฆ
On matroids of the greatestW-connectivity
โ Scribed by Li Weixuan
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 407 KB
- Volume
- 35
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
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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 prov