Colouring simplicial complexes via the Lechuga-Murillo's model

L. Lechuga and A. Murillo showed that a non-oriented, simple, connected, finite graph $G$ is $k$-colourable if and only if a certain pure Sullivan algebra associated to $G$ and $k$ is not elliptic. In this paper, we extend this result to simplicial complexes by means of several notions of colourings of these objects.

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