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

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-con...

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Bibliographic Details
Published in:Logical Methods in Computer Science
Main Author: Bruno Courcelle
Format: Article
Language:English
Published: Logical Methods in Computer Science e.V. 2006-03-01
Subjects:
computer science - logic in computer science
f.4.1
Online Access:https://lmcs.episciences.org/2250/pdf
Description
Summary: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.
ISSN:1860-5974

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