منابع مشابه
Essentially Infinite Colourings of Hypergraphs
We consider edge colourings of the complete r-uniform hypergraph K (r) n on n vertices. How many colours may such a colouring have if we restrict the number of colours locally? The local restriction is formulated as follows: for a fixed hypergraph H and an integer k we call a colouring (H, k)-local if every copy of H in the complete hypergraph K (r) n receives at most k different colours. We in...
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Let the bicoloring cover number χ(G) for a hypergraph G(V,E) be the minimum number of bicolorings of vertices of G such that every hyperedge e ∈ E of G is properly bicolored in at least one of the χ(G) bicolorings. We establish a tight bound for χ(K n), where K n is the complete k-uniform hypergraph on n vertices. We investigate the relationship between χ(G), matchings, hitting sets, α(G)(indep...
متن کاملMinimal Covers of Formal Languages
Let L1; L2 be languages. If L1 L2, then we say that L2 covers L1. Let C;D be classes of languages over . We call a cover L2 2 C of L1 a C-minimal cover with respect to D if, for all L0 2 C, L1 L0 L2 implies L2 L0 2 D. We examine in detail the particular cases of minimal regular covers and minimal context-free covers, both with respect to nite languages. The closure properties of the class of la...
متن کاملOn splitting infinite-fold covers
Let X be a set, κ be a cardinal number and let H be a family of subsets of X which covers each x ∈ X at least κ times. What assumptions can ensure that H can be decomposed into κ many disjoint subcovers? We examine this problem under various assumptions on the set X and on the cover H: among other situations, we consider covers of topological spaces by closed sets, interval covers of linearly o...
متن کاملMinimal Covers and Arithmetical Sets1
If a and b are degrees of unsolvability, a is called a minimal cover of b if b<a and no degree c satisfies b<c<a. The degree a is called a minimal cover if it is a minimal cover of some degree b. We prove by a very simple argument that 0" is not a minimal cover for any n. From this result and the axiom of Borel determinateness (BD) we show that the degrees of arithmetical sets (with their usual...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.06.014