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

lmcs:2250 - Logical Methods in Computer Science, March 23, 2006, Volume 2, Issue 2
The monadic second-order logic of graphs XVI : Canonical graph<br> decompositions

Authors: Courcelle, Bruno

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.


Source : oai:arXiv.org:cs/0510066
DOI : 10.2168/LMCS-2(2:2)2006
Volume: Volume 2, Issue 2
Published on: March 23, 2006
Submitted on: June 24, 2005
Keywords: Computer Science - Logic in Computer Science,F.4.1


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