The monadic second-order logic of graphs XVI : Canonical graph<br> decompositions

Details The monadic second-order logic of graphs XVI : Canonical graph<br> decompositions The monadic second-order logic of graphs XVI : Canonical graph<br> decompositions

2005-10-22

arxiv.org/abs/cs/0510066v3

LMCS 2 (2:2) 2006

Computer Science

Logic in Computer Science

Scientific paper

10.2168/LMCS-2(2:2)2006

This article establishes that the split decomposition of graphs introduced by Cunnigham, is definable in Monadic Second-Order Logic.This result is actually an instance of a more general result covering canonical graph decompositions like the modular decomposition and the Tutte decomposition of 2-connected graphs into 3-connected components. As an application, we prove that the set of graphs having the same cycle matroid as a given 2-connected graph can be defined from this graph by Monadic Second-Order formulas.

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