Displaying similar documents to “On a conjecture of Frankl and Füredi.”

Downhill Domination in Graphs

Teresa W. Haynes, Stephen T. Hedetniemi, Jessie D. Jamieson, William B. Jamieson (2014)

Discussiones Mathematicae Graph Theory

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A path π = (v1, v2, . . . , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi) ≥ deg(vi+1), where deg(vi) denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number...

Sharper ABC-based bounds for congruent polynomials

Daniel J. Bernstein (2005)

Journal de Théorie des Nombres de Bordeaux

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Agrawal, Kayal, and Saxena recently introduced a new method of proving that an integer is prime. The speed of the Agrawal-Kayal-Saxena method depends on proven lower bounds for the size of the multiplicative semigroup generated by several polynomials modulo another polynomial h . Voloch pointed out an application of the Stothers-Mason ABC theorem in this context: under mild assumptions, distinct polynomials A , B , C of degree at most 1 . 2 deg h - 0 . 2 deg rad A B C cannot all be congruent modulo h . This paper presents two...