Definable decompositions for graphs of bounded linear cliquewidthArticle
Authors: Mikołaj Bojańczyk ; Martin Grohe ; Michał Pilipczuk
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Mikołaj Bojańczyk;Martin Grohe;Michał Pilipczuk
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.