Dirac's theorem on simplicial matroids
  We introduce the notion of k-hyperclique complexes, i.e., the largest simplicial complexes on the set [n] with a fixed k-skeleton. These simplicial complexes are a higher-dimensional analogue of clique (or flag) complexes (case k=2) and they are a rich new class of simplicial complexes.   We show that Dirac's theorem on chordal graphs has a higher-dimensional analogue in which graphs and clique complexes get replaced, respectively, by simplicial matroids and k-hyperclique complexes. We prove also a higher-dimensional analogue of Stanley's reformulation of Dirac's theorem on chordal graphs. 
Raul Cordovil (Dept.Math.-IST, Portugal), Manoel Lemos   (Dept.Math.-UFP, Pernambuco, Brasil) and Claudia Linhares Sales   (...