The journey of the union-closed sets conjecture

DOI10.1007/s00373-014-1515-0zbMath1327.05249arXiv1309.3297OpenAlexW2138776194WikidataQ55969511 ScholiaQ55969511MaRDI QIDQ897265

Oliver Schaudt, Henning Bruhn

Publication date: 17 December 2015

Published in: Graphs and Combinatorics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1309.3297

zbMATH Keywords

graphslatticesFrankl's conjectureunion-closed

Mathematics Subject Classification ID

Hypergraphs (05C65) Permutations, words, matrices (05A05)

Related Items (19)

Verifying Faradžev-Read Type Isomorph-Free Exhaustive Generation ⋮ New conjectures for union-closed families ⋮ The union-closed sets conjecture for small families ⋮ Frankl's conjecture for subgroup lattices ⋮ Unnamed Item ⋮ On the union-closed sets conjecture ⋮ Union-closed sets and Horn Boolean functions ⋮ Spanoids---An Abstraction of Spanning Structures, and a Barrier for LCCs ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Extremal union-closed set families ⋮ Cutting planes for families implying Frankl’s conjecture ⋮ Spanoids - An Abstraction of Spanning Structures, and a Barrier for LCCs ⋮ Well-graded families and the union-closed sets conjecture ⋮ Generation of Union Closed Sets and Moore families ⋮ Unnamed Item ⋮ An Asymptotic Version of Frankl’s Conjecture ⋮ Zeon and idem-Clifford formulations of hypergraph problems ⋮ Small sets in union-closed families

Cites Work

• The graph formulation of the union-closed sets conjecture
• Minimal weight in union-closed families
• A new short proof for the Kruskal-Katona theorem
• FC-families and improved bounds for Frankl's conjecture
• The 11-element case of Frankl's conjecture
• On the scope of averaging for Frankl's conjecture
• On averaging Frankl's conjecture for large union-closed-sets
• On the density of sets of vectors
• Union-closed families
• Density of union-closed families
• Extremal properties of collections of subsets containing no two sets and their union
• Frankl's conjecture is true for modular lattices
• An inequality for the sizes of prime filters of finite distributive lattices
• On the trace of finite sets
• Families implying the Frankl conjecture
• Excess of a lattice
• Strong semimodular lattices and Frankl's conjecture
• On Conway's recursive sequence
• Lower semimodular types of lattices: Frankl's conjecture holds for lower quasi-semimodular lattices
• Frankl's conjecture is true for lower semimodular lattices
• An extremal problern for set families generated with the union and symmetric difference operations
• Inequalities for cross-unions of collections of finite sets
• Formalizing Frankl’s Conjecture: FC-Families
• An attempt at frankl’s conjecture
• Conway's Challenge Sequence
• A graph-theoretic version of the union-closed sets conjecture
• An Average Set Size Theorem
• On union-closed sets and Conway's sequence
• On conjectures of Frankl and El‐Zahar
• The union-closed sets conjecture almost holds for almost all random bipartite graphs
• Union-closed families of sets
• Union-closed families of sets
• On union-closed families. I
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: The journey of the union-closed sets conjecture