A problem of P. Seymour on nonbinary matroids

Abstract

The following statement fork=1, 2, 3 has been proved by Tutte [4], Bixby [1] and Seymour [3] respectively: IfM is ak-connected non-binary matroid andX a set ofk-1 elements ofM, thenX is contained in someU 24 minor ofM. Seymour [3] asks whether this statement remains true fork=4; the purpose of this note is to show that it does not and to suggest some possible alternatives.

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References

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Supported in part by the National Science Foundation

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Kahn, J. A problem of P. Seymour on nonbinary matroids. Combinatorica 5, 319–323 (1985). https://doi.org/10.1007/BF02579246

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AMS subject classification

  • 05 B 35