Lechuga and 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.

中文翻译：

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通过 Lechuga-Murillo 模型为单纯复形着色

Lechuga 和 Murillo 证明了一个无向的、简单的、连通的、有限的图 G 是 k 可着色的，当且仅当与 G 和 k 相关联的某个纯 Sullivan 代数不是椭圆的。在本文中，我们通过这些对象的几种着色概念将这一结果扩展到单纯复形。