Bounding the Number of Minimal Transversals in Tripartite 3-Uniform Hypergraphs
نویسندگان
چکیده
We focus on the maximum number of minimal transversals in 3-partite 3-uniform hypergraphs n vertices. Those (and their transversals) are commonly found database applications. In this paper we prove that grows at least like 1.4977^n and most 1.5012^n.
منابع مشابه
On the number of minimal transversals in 3-uniform hypergraphs
We prove that the number of minimal transversals (and also the number of maximal independent sets) in a 3-uniform hypergraph with n vertices is at most c, where c ≈ 1.6702. The best known lower bound for this number, due to Tomescu, is ad, where d = 10 1 5 ≈ 1.5849 and a is a constant.
متن کاملTransversals in 4-Uniform Hypergraphs
Let H be a 4-uniform hypergraph on n vertices. The transversal number τ(H) of H is the minimum number of vertices that intersect every edge. The result in [J. Combin. Theory Ser. B 50 (1990), 129–133] by Lai and Chang implies that τ(H) 6 7n/18 when H is 3-regular. The main result in [Combinatorica 27 (2007), 473–487] by Thomassé and Yeo implies an improved bound of τ(H) 6 8n/21. We provide a fu...
متن کاملEnumerating Minimal Transversals of Geometric Hypergraphs
We consider the problem of enumerating all minimal hitting sets of a given hypergraph (V,R), where V is a finite set, called the vertex set andR is a set of subsets of V called the hyperedges. We show that, when the hypergraph admits a balanced subdivision, then a recursive decomposition can be used to obtain efficiently all minimal hitting sets of the hypergraph. We apply this decomposition fr...
متن کاملThe Ramsey Number of Loose Paths in 3-Uniform Hypergraphs
Recently, asymptotic values of 2-color Ramsey numbers for loose cycles and also loose paths were determined. Here we determine the 2-color Ramsey number of 3-uniform loose paths when one of the paths is significantly larger than the other: for every n > ⌊ 5m 4 ⌋ , we show that R(P n,P m) = 2n + ⌊m + 1 2 ⌋ .
متن کاملTransversals in uniform hypergraphs with property (7, 2)
Let f(r; p; t) (p¿ t¿1, r¿2) be the maximum of the cardinality of a minimum transversal over all r-uniform hypergraphs H possessing the property that every subhypergraph of H with p edges has a transversal of size t. The values of f(r; p; 2) for p=3; 4; 5; 6 were found in Erdős et al. (Siberian Adv. Math. 2 (1992) 82–88). We give bounds on f(r; 7; 2), partially answering a question in Erdős et ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discrete Mathematics & Theoretical Computer Science
سال: 2023
ISSN: ['1365-8050', '1462-7264']
DOI: https://doi.org/10.46298/dmtcs.7129