Pure flag simplicial complexes and the Erd\H{o}s-Ko-Rado-property
Jorge Alberto Olarte, Francisco Santos, Jonathan Spreer, Christian Stump · arXiv (Cornell University) · 2017
We launch the thorough study of the pure Erd\H{o}s-Ko-Rado property of simplicial complexes. Specifically, we identify two fundamental conditions on the maximal faces of a pure simplicial complex to satisfy the Erd\H{o}s-Ko-Rado property, namely flagness and the absence of boundary ridges. We establish a tower of increasingly ambitious conjectures stating, in the most general form, that these properties are sufficient to establish the pure-EKR property in arbitrary dimension. We then prove this conjecture in dimensions two and three.