Well-graded families and the union-closed sets conjecture
The electronic journal of combinatorics, Tome 27 (2020) no. 1
The union-closed sets conjecture states that if a finite family of sets $\mathcal{F}$ is union-closed, then there must be some element contained in at least half of the sets of $\mathcal{F}$. In this work we study the relationship between the union-closed sets conjecture and union-closed families that have the property of being well-graded. In doing so, we show how the density and other properties are affected by the extra structure contained in well-graded families, and we also give several conditions under which well-graded families satisfy the union-closed sets conjecture.
DOI :
10.37236/8380
Classification :
05D05, 06A07
Mots-clés : well-graded union-closed families, knowledge spaces
Mots-clés : well-graded union-closed families, knowledge spaces
Affiliations des auteurs :
Jeffrey Matayoshi 1
@article{10_37236_8380,
author = {Jeffrey Matayoshi},
title = {Well-graded families and the union-closed sets conjecture},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/8380},
zbl = {1507.05096},
url = {http://geodesic.mathdoc.fr/articles/10.37236/8380/}
}
Jeffrey Matayoshi. Well-graded families and the union-closed sets conjecture. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/8380
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