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JCT
2007

Vertex-minors, monadic second-order logic, and a conjecture by Seese

9 years 11 months ago
Vertex-minors, monadic second-order logic, and a conjecture by Seese
We prove that one can express the vertex-minor relation on finite undirected graphs by formulas of monadic second-order logic (with no edge set quantification) extended with a predicate expressing that a set has even cardinality. We obtain a slight weakening of a conjecture by Seese stating that sets of graphs having a decidable satisfiability problem for monadic second-order logic have bounded clique-width. We also obtain a polynomial-time algorithm to check that the rank-width of a graph is at most k for any fixed k. The proofs use isotropic systems. Key words: Clique-width, Rank-width, Monadic second-order logic, Seese’s conjecture, Local complementation, Vertex-minor, Isotropic system
Bruno Courcelle, Sang-il Oum
Added 15 Dec 2010
Updated 15 Dec 2010
Type Journal
Year 2007
Where JCT
Authors Bruno Courcelle, Sang-il Oum
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