Preprints
Citation counts are taken from Google Scholar, which on occasion overcounts slightly.
- Denys Bulavka and Russ Woodroofe, Strict Erdős-Ko-Rado theorems for simplicial complexes, preprint.
We show that if a simplicial complex is a near-cone of sufficiently high depth, then the only maximum families of small pairwise intersecting faces are those with a common intersection. Thus, near-cones of sufficiently high depth satisfy the strict Erdős-Ko-Rado property conjectured by Holroyd and Talbot and by Borg. One consequence is a strict Erdős-Ko-Rado theorem for independence complexes of chordal graphs with an isolated vertex. Under stronger shiftedness conditions, we prove a sharper stability theorem of Hilton-Milner type, as well as two cross-intersecting theorems.
- Denys Bulavka and Russ Woodroofe, A short proof of the Hilton-Milner Theorem, preprint.
We give a short and relatively elementary proof of the Hilton-Milner Theorem.
- Denys Bulavka, Francesca Gandini, and Russ Woodroofe, A Hilton-Milner theorem for exterior algebras, preprint.
Recent work of Scott and Wilmer and of Woodroofe extends the Erdős-Ko-Rado theorem from set systems to subspaces of k-forms in an exterior algebra. We prove an extension of the Hilton-Milner theorem to the exterior algebra setting, answering in a strong way a question asked by these authors.