Simplicial Lusternik-Schnirelmann category
  The simplicial LS-category of a finite abstract simplicial complex is a new invariant of the strong homotopy type, defined in purely combinatorial terms, that generalizes to arbitrary simplicial complexes the well known notion of arboricity of a graph, and that allows to develop all the machinery of algebraic topology which is costumary in the classical theory of Lusternik-Schnirelmann category. 
Desamparados Fern\'andez-Ternero, Enrique Mac\'ias-Virg\'os, Erika   Minuz, Jos\'e Antonio Vilches
math.AT