Decidability of modal logics of non-k-colorable graphs

03/17/2023

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by   Ilya Shapirovsky, et al.

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