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Fixed-point logics on planar graphs

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1 Author(s)
Grohe, M. ; Inst. fur Math. Logik, Albert-Ludwigs-Univ., Freiburg, Germany

We study the expressive power of inflationary fixed-point logic IFP and inflationary fixed-point logic with counting IFP+C on planar graphs. We prove the following results: (1) IFP captures polynomial time on 3-connected planar graphs, and IFP+C captures polynomial time on arbitrary planar graphs. (2) Planar graphs can be characterized up to isomorphism in a logic with finitely many variables and counting. This answers a question of Immerman (1987). (3) The class of planar graphs is definable in IFP. This answers a question of Dawar and Gradel

Published in:

Logic in Computer Science, 1998. Proceedings. Thirteenth Annual IEEE Symposium on

Date of Conference:

21-24 Jun 1998