Weight choosability of oriented hypergraphs
نویسندگان
چکیده
منابع مشابه
Choosability in Random Hypergraphs
The choice number of a hypergraph H = (V, E) is the least integer s for which for every family of color lists S = {S(v) : v ∈ V }, satisfying |S(v)| = s for every v ∈ V , there exists a choice function f so that f(v) ∈ S(v) for every v ∈ V , and no edge of H is monochromatic under f . In this paper we consider the asymptotic behavior of the choice number of a random k-uniform hypergraph H(k, n,...
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ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...
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Suppose the edges and the vertices of a simple graph G are assigned k-element lists of real weights. By choosing a representative of each list, we specify a vertex colouring, where for each vertex its colour is defined as the sum of the weights of its incident edges and the weight of the vertex itself. How long lists ensures a choice implying a proper vertex colouring for any graph? Is there an...
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A total-weighting of a graph G = (V,E) is a mapping f which assigns to each element y ∈ V ∪ E a real number f(y) as the weight of y. A total-weighting f of G is proper if the colouring φf of the vertices of G defined as φf (v) = f(v) + ∑ e∋v f(e) is a proper colouring of G, i.e., φf (v) ̸= φf (u) for any edge uv. For positive integers k and k′, a graph G is called (k, k′)-total-weight-choosable ...
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ژورنال
عنوان ژورنال: Ars Mathematica Contemporanea
سال: 2018
ISSN: 1855-3974,1855-3966
DOI: 10.26493/1855-3974.1317.745