Sep 21, 2012 · Abstract:This paper extends the scenario of the Four Color Theorem in the following way. Let H(d,k) be the set of all k-uniform hypergraphs ...

Oct 17, 2014 · This paper extends the scenario of the Four Color Theorem in the following way. Let H d , k be the set of all k -uniform hypergraphs that ...

A k-uniform hypergraph H is said to be d-embeddable if there exists an embedding of. H into Rd. Also, we denote by Hd,k the set of all d-embeddable k-uniform ...

Definition. For d, k, n in ℕ define. 𝜒𝑑,𝑘. 𝑛 = max 𝜒 𝐻 : 𝑉 𝐻 = 𝑛,𝐻 ∈ ℋ𝑑,𝑘 to be the maximum (weak) chromatic number of a d-embeddable k-uniform hypergraph ...

Aug 29, 2014 · A k-uniform hypergraph H is said to be d-embeddable if there exists an embedding of H into Rd. Also, we denote by Hd,k the set of all d- ...

We investigate lower and upper bounds on the maximum (weak and strong) chromatic number of hypergraphs in H d,k. For example, we can prove that for d ≥ 3 there ...

This paper investigates lower and upper bounds on the maximum (weak) chromatic number of hypergraphs in the set of all k-uniformhypergraphs that can be ...

Let H d,k be the set of all k-uniform hypergraphs that can be linearly embedded into ℝd. We investigate lower and upper bounds on the maximum (weak and strong) ...

Coloring d-embeddable k-uniform hypergraphs ; Journal Article · Q Science > QA Mathematics · Faculty of Science, Engineering and Medicine > Science > Mathematics.

We introduce the notion of a co-edge of a hypergraph, which is a subset of vertices to be colored so that at least two vertices are of the same color.