arXiv subjects

Jorge Olarte

Publications and source records attributed to Jorge Olarte.

2 recordsLinked to original sources

arXiv2018

Short proof of two cases of Chvátal's conjecture

In 1974 Chvátal conjectured that no intersecting family $\mathcal{F}$ in a downset can be larger than the largest star. In the same year Kleitman and Magnanti proved the conjecture when $\mathcal{F}$ is contained in the union of two stars, and Sterboul when $\operatorname{rank}(\mathcal{F})\le 3$. We give short self-contained proofs of these two statements.

math.CO↗

arXiv2018

The EKR property for flag pure simplicial complexes without boundary

We prove that the family of facets of a pure simplicial complex of dimension up to three satisfies the Erdős-Ko-Rado property whenever it is flag and has no boundary ridges. We conjecture the same to be true in arbitrary dimension and give evidence for this conjecture. Our motivation is that complexes with these two properties include flag pseudo-manifolds and cluster complexes.

math.CO↗