On the edge-colouring problem for unions of complete uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Edge coloring complete uniform hypergraphs with many components
Let H be a hypergraph. For a k-edge coloring c : E(H) → {1, . . . , k} let f(H, c) be the number of components in the subhypergraph induced by the color class with the least number of components. Let fk(H) be the maximum possible value of f(H, c) ranging over all k-edge colorings of H . If H is the complete graph Kn then, trivially, f1(Kn) = f2(Kn) = 1. In this paper we prove that for n ≥ 6, f3...
متن کاملThe α-Arboricity of Complete Uniform Hypergraphs
α-acyclicity is an important notion in database theory. The α-arboricity of a hypergraphH is the minimum number of α-acyclic hypergraphs that partition the edge set of H. The α-arboricity of the complete 3-uniform hypergraph is determined completely.
متن کاملImproved Bounds for Covering Complete Uniform Hypergraphs
We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...
متن کاملAppendix: On Edge-Isoperimetric Theorems for Uniform Hypergraphs
Denote by Ω = {1, . . . , n} an n–element set. For all A,B ∈ Ωk ) , the k–element subsets of Ω, define the relation ∼ as follows: A ∼ B iff A and B have a common shadow, i.e. there is a C ∈ ( Ω k−1 ) with C ⊂ A and C ⊂ B. For fixed integer α, our goal is to find a family A of k–subsets with size α, having as many as possible ∼ –relations for all pairs of its elements. For k = 2 this was achieve...
متن کاملHamiltonian decompositions of complete k-uniform hypergraphs
Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, we define a new notion of a Hamiltonian decomposition of a uniform hypergraph. We then consider the problem of constructing such decompositions for complete uniform hypergraphs, and describe its relationship with other topics, such as design theory.
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
سال: 1981
ISSN: 0012-365X
DOI: 10.1016/0012-365x(81)90003-0