Erdős-Ko-Rado Type Theorems for Simplicial Complexes

It is shown that every shifted simplicial complex ∆ is EKR of type (r, s), provided that the size of every facet of ∆ is at least (2s + 1)r − s. It is moreover proven that every i-near-cone simplicial complex is EKR of type (r, i) if depthK∆ > (2i + 1)r − i − 1, for some field K. Furthermore, we prove that if G is a graph having at least (2i + 1)r − i connected components, including i isolated vertices, then its independence simplicial complex ∆G is EKR of type (r, i). The results of this paper, generalize the main result of Frankl (2013).