Abstract
In our paper, we prove that Graph Connectivity is not in Monadic NP even in the presence of a built-in relation of arbitrary degree that does not have for an arbitrary, but fixed k ≥ 2 ∈ IN the complete graph K k as a minor. We obtain our result by using the method of indiscernibles and giving a winning strategy for the duplicator in the Ajtai-Fagin Ehrenfeucht-Fraïssé Game .
The result is afterwards strengthened to arbitrary forbidden minors and to minor-closed classes of binary relations.
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Kreidler, M., Seese, D. (1999). Monadic NP and Graph Minors. In: Gottlob, G., Grandjean, E., Seyr, K. (eds) Computer Science Logic. CSL 1998. Lecture Notes in Computer Science, vol 1584. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10703163_9
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DOI: https://doi.org/10.1007/10703163_9
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