The monadic second-order logic of graphs XVI : Canonical graph<br> decompositions
<|reference_start|>The monadic second-order logic of graphs XVI : Canonical graph<br> 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-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.<|reference_end|>
@article{courcelle2005the,
    title={The monadic second-order logic of graphs XVI : Canonical graph<br>
  decompositions},
    author={Bruno Courcelle},
    journal={Logical Methods in Computer Science, Volume 2, Issue 2 (March 23,
  2006) lmcs:2250},
    year={2005},
    doi={10.2168/LMCS-2(2:2)2006},
    archivePrefix={arXiv},
    eprint={cs/0510066},
    primaryClass={cs.LO}
}