English

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}
}
R2 v1 2026-06-23T00:54:43.970Z