Helly number, domination and homology
Journal of Algebraic Combinatorics, cilt.64, sa.3, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 64 Sayı: 3
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s10801-026-01586-9
- Dergi Adı: Journal of Algebraic Combinatorics
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Helly number, Homological connectivity, Induced matching number, Leray number, Strong domination number
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
The Helly number h(H) of a hypergraph H whose edges have no vertex in common is the size of its largest inclusion-wise minimal subhypergraph with empty intersection. We prove that the homological connectivity of the independence complex of H can be bounded in terms of its number of vertices and the Helly number of its complementary hypergraph Hc. Our proof relies on an interconnection between the Helly number and a domination parameter of hypergraphs. Separately, we provide an upper bound to the Leray number of the noncover complex of any hypergraph H without any isolated vertex involving the strong domination number of H.