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Some Hard Problems on Matroid Spikes

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Abstract

Spikes form an interesting class of 3-connected matroids of branch-width 3. We show that some computational problems are hard on spikes with given matrix representations over infinite fields. Namely, the question whether a given spike is the free spike is co-NP-hard (though the property itself is definable in monadic second-order logic); and the task to compute the Tutte polynomial of a spike is #P-hard (even though that can be solved efficiently on all matroids of bounded branch-width which are represented over a finite field).

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  1. Department of Computer Science, VSB - Technical University Ostrava, 17. listopadu 15, 708 33 Ostrava and Faculty of Informatics, Masaryk University in Brno, Botanicka 68a, 602 00 Brno, Czech Republic

    Petr Hlineny

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  1. Petr Hlineny
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Correspondence to Petr Hlineny.

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Hlineny, P. Some Hard Problems on Matroid Spikes. Theory Comput Syst 41, 551–562 (2007). https://doi.org/10.1007/s00224-007-1307-5

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  • DOI: https://doi.org/10.1007/s00224-007-1307-5

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