Clonal Ding–Oporowski–Oxley–Vertigan-type minor conjecture

Let mm be a positive integer, and let MM be a 33-connected clonal matroid. The matroids U2,2mU_{2,2m} and U2m2,2mU_{2m-2,2m} are uniform matroids, while Λm\Lambda_m and Δm\Delta_m denote the named matroids used in the source. Clonal minor conjecture. There is a function f(m)f(m) such that, if MM has at least f(m)f(m) elements, then MM has one of the following as a clonal minor: U2,2mU_{2,2m}, U2m2,2mU_{2m-2,2m}, Λm\Lambda_m, or Δm\Delta_m.

The conjecture is presented as a possible strengthening of the theorem proved in the chapter: the desired conclusion is that one of these structured minors can be found while retaining clonal structure. No resolution is given in the supplied text.

Sources & referencesView supporting material

Primary source

Jim Geelen and Geoff Whittle, “Inequivalent Representations of Matroids over Prime Fields”, arXiv:1101.4683 (2011).

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