English

Decidability of modal logics of non-$k$-colorable graphs

Logic 2023-08-07 v3 Logic in Computer Science

Abstract

We consider the bimodal language, where the first modality is interpreted by a binary relation in the standard way, and the second is interpreted by the relation of inequality. It follows from Hughes (1990), that in this language, non-kk-colorability of a graph is expressible for every finite kk. We show that modal logics of classes of non-kk-colorable graphs (directed or non-directed), and some of their extensions, are decidable.

Keywords

Cite

@article{arxiv.2303.09934,
  title  = {Decidability of modal logics of non-$k$-colorable graphs},
  author = {Ilya Shapirovsky},
  journal= {arXiv preprint arXiv:2303.09934},
  year   = {2023}
}