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--colorability of a graph is expressible for every finite . We show that modal logics of classes of non--colorable graphs (directed or non-directed), and some of their extensions, are decidable.
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}
}