科研之友
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摘要
For a matroid N, a matroid M is N-connected if every two elements of M are in an N-minor together. Thus a matroid is connected if and only if it is U-1,U-2-connected. This paper proves that U-1,U-2 is the only connected matroid N such that if M is N-connected with vertical bar E(M)vertical bar>vertical bar E(N)vertical bar, then M\e or M/e is N-connected for all elements e. Moreover, we show that U-1,U-2 and M(W-2) are the only matroids N such that, whenever a matroid has an N-minor using {e, f} and an N-minor using {f, g}, it also has an N-minor using {e, g}. Finally, we show that M is U-0,U-1 circle plus U-1,U-1-connected if and only if every clonal class of M is trivial.
- 出版日期2018-9
