Definable decompositions for graphs of bounded linear cliquewidth
Logic in Computer Science
2023-06-22 v5
Abstract
We prove that for every positive integer k, there exists an MSO_1-transduction that given a graph of linear cliquewidth at most k outputs, nondeterministically, some cliquewidth decomposition of the graph of width bounded by a function of k. A direct corollary of this result is the equivalence of the notions of CMSO_1-definability and recognizability on graphs of bounded linear cliquewidth.
Keywords
Cite
@article{arxiv.1803.05937,
title = {Definable decompositions for graphs of bounded linear cliquewidth},
author = {Mikołaj Bojańczyk and Martin Grohe and Michał Pilipczuk},
journal= {arXiv preprint arXiv:1803.05937},
year = {2023}
}