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arXiv · 2412.04970

CMSO-transducing tree-like graph decompositions

Rutger Campbell·Bruno Guillon·Mamadou Moustapha Kanté·Eun Jung Kim·Noleen Köhler
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Abstract

We give $\operatorname{CMSO}$-transductions that, given a graph $G$, output its modular decomposition, its split decomposition and its bi-join decomposition. This improves results by Courcelle [Logical Methods in Computer Science, 2006] who gave such transductions using order-invariant $\operatorname{MSO}$, a strictly more expressive logic than $\operatorname{CMSO}$. Our methods more generally yield $\operatorname{C}_2 \operatorname{MSO}$-transductions that output the canonical decompositions of weakly-partitive set systems and weakly-bipartitive systems of bipartitions.

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Rutger Campbell, Bruno Guillon, Mamadou Moustapha Kanté, Eun Jung Kim, Noleen Köhler. 2024-12-06. CMSO-transducing tree-like graph decompositions. https://arxiv.org/abs/2412.04970

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