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Markov, Minko, Haralampiev, Vladislav, Georgiev, Georgi (2015)
Serdica Journal of Computing
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We investigate a recently introduced width measure of planar shapes called sweepwidth and prove a lower bound theorem on the sweepwidth.
Wacław Szymański (1977)
Annales Polonici Mathematici
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L. Gajek (1987)
Applicationes Mathematicae
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J. Kaczorowski, A. Perelli (2012)
Acta Arithmetica
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Tsz Ho Chan (2006)
Acta Arithmetica
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Ivan Chajda (2007)
Discussiones Mathematicae - General Algebra and Applications
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The concept of a commutative directoid was introduced by J. Ježek and R. Quackenbush in 1990. We complete this algebra with involutions in its sections and show that it can be converted into a certain implication algebra. Asking several additional conditions, we show whether this directoid is sectionally complemented or whether the section is an NMV-algebra.
Bert L. Hartnell, Douglas F. Rall (2003)
Discussiones Mathematicae Graph Theory
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The study of domination in Cartesian products has received its main motivation from attempts to settle a conjecture made by V.G. Vizing in 1968. He conjectured that γ(G)γ(H) is a lower bound for the domination number of the Cartesian product of any two graphs G and H. Most of the progress on settling this conjecture has been limited to verifying the conjectured lower bound if one of the graphs has a certain structural property. In addition, a number of authors have established bounds...
Olivier Ramaré (2001)
Acta Arithmetica
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Paturi, R., Pudlák, P. (2004)
Zapiski Nauchnykh Seminarov POMI
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Shabnam Akhtari, Jeffrey D. Vaaler (2016)
Acta Arithmetica
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We prove inequalities that compare the size of an S-regulator with a product of heights of multiplicatively independent S-units. Our upper bound for the S-regulator follows from a general upper bound for the determinant of a real matrix proved by Schinzel. The lower bound for the S-regulator follows from Minkowski's theorem on successive minima and a volume formula proved by Meyer and Pajor. We establish similar upper bounds for the relative regulator of an extension l/k of number fields. ...
Vladimir Volenec (1987)
Stochastica
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A laterally commutative heap can be defined on a given set iff there is the structure of a TST-space on this set.
Kulikov, A.S., Fedin, S.S. (2004)
Zapiski Nauchnykh Seminarov POMI
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Rechnoi, V. (2005)
Lobachevskii Journal of Mathematics
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Paul Dorbec, Sylvain Gravier, Sandi Klavžar, Simon Spacapan (2006)
Discussiones Mathematicae Graph Theory
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Upper and lower bounds on the total domination number of the direct product of graphs are given. The bounds involve the {2}-total domination number, the total 2-tuple domination number, and the open packing number of the factors. Using these relationships one exact total domination number is obtained. An infinite family of graphs is constructed showing that the bounds are best possible. The domination number of direct products of graphs is also bounded from below.
Bert L. Hartnell, Douglas F. Rall (2004)
Discussiones Mathematicae Graph Theory
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In this paper we consider the Cartesian product of an arbitrary graph and a complete graph of order two. Although an upper and lower bound for the domination number of this product follow easily from known results, we are interested in the graphs that actually attain these bounds. In each case, we provide an infinite class of graphs to show that the bound is sharp. The graphs that achieve the lower bound are of particular interest given the special nature of their dominating sets and...