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Greedy Rankings and Arank Numbers
, 2009
"... A ranking on a graph is an assignment of positive integers to its vertices such that any path between two vertices of the same rank contains a vertex of strictly larger rank. A ranking is locally minimal if reducing the rank of any single vertex produces a non ranking. A ranking is globally minimal ..."
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one property it satisfies all three. As a consequence of this and known results on arank numbers of paths we improve known upper bounds for online ranking. 1
Minimal rankings and the arank number of a path
, 2003
"... Given a graph G, a function f: V (G) → {1, 2,..., k} is a kranking of G if f(u) = f(v) implies every u − v path contains a vertex w such that f(w)> f(u). A kranking is minimal if the reduction of any label greater than 1 violates the described ranking property. The arank number of a graph, den ..."
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Given a graph G, a function f: V (G) → {1, 2,..., k} is a kranking of G if f(u) = f(v) implies every u − v path contains a vertex w such that f(w)> f(u). A kranking is minimal if the reduction of any label greater than 1 violates the described ranking property. The arank number of a graph
MINIMAL RANKINGS OF THE CARTESIAN PRODUCT Kn Km
 DISCUSSIONES MATHEMATICAE GRAPH THEORY
, 2012
"... For a graph G = (V,E), a function f: V (G) → {1, 2,..., k} is a kranking if f(u) = f(v) implies that every u−v path contains a vertex w such that f(w)> f(u). A kranking is minimal if decreasing any label violates the definition of ranking. The arank number, ψr(G), of G is the maximum value of ..."
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For a graph G = (V,E), a function f: V (G) → {1, 2,..., k} is a kranking if f(u) = f(v) implies that every u−v path contains a vertex w such that f(w)> f(u). A kranking is minimal if decreasing any label violates the definition of ranking. The arank number, ψr(G), of G is the maximum value
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, 2003
"... Given a graph G, a function f: V (G) → {1, 2,..., k} is a kranking of G if f(u) = f(v) implies every u − v path contains a vertex w such that f(w)> f(u). A kranking is minimal if the reduction of any label greater than 1 violates the described ranking property. The arank number of a graph, den ..."
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Given a graph G, a function f: V (G) → {1, 2,..., k} is a kranking of G if f(u) = f(v) implies every u − v path contains a vertex w such that f(w)> f(u). A kranking is minimal if the reduction of any label greater than 1 violates the described ranking property. The arank number of a graph
Right Type Departmental Bulletin Paper
"... Abstract. We introduce atheoretical test, named weight discrepancy test, on pseudorandom number generators. This test measures the $\chi^{2}$discrepancy between the distribution of the number of ones in some specified bits in the generated sequence and the binomial distribution, under the assumptio ..."
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Abstract. We introduce atheoretical test, named weight discrepancy test, on pseudorandom number generators. This test measures the $\chi^{2}$discrepancy between the distribution of the number of ones in some specified bits in the generated sequence and the binomial distribution, under