2 research outputs found
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.Comment: 11 pages; Annals of Combinatorics, to appea