منابع مشابه
Building counterexamples
A conjecture concerning perfect graphs asserts that if for a Berge graph G the following three conditions hold: 1. neither G, nor Ḡ has an even pair; 2. neither G, nor Ḡ has a stable cutset; 3. neither G, nor Ḡ has a star-cutset, then G or Ḡ is diamond-free. We show that this conjecture is not valid and that, in a way, every weaker version is false too. To this end, we construct a class of perf...
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Taking an extension of resolution as a base calculus (though its principles are applicable to other calculi) for searching proofs (refuta-tions) and counterexamples (models), we introduce a new method able to nd refutations and also models by analogy with refutations and models in a knowledge base. The source objects for the analogy process are generalizations of the refutations (models). They ...
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In the following text for arbitrary $X$ with at least two elements, nonempty countable set $Gamma$ we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map. We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney, exact Dev...
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The classical Ritt’s Theorems state several properties of univariate polynomial decomposition. In this paper we present new counterexamples to the first Ritt theorem, which states the equality of length of decomposition chains of a polynomial, in the case of rational functions. Namely, we provide an explicit example of a rational function with coefficients in Q and two decompositions of differe...
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We explore M. Gromov's counterexamples to systolic inequalities. Does the manifold S 2 × S 2 admit metrics of arbitrarily small volume such that every noncontractible surface inside it has at least unit area? This question is still open, but the answer is affirmative for its analogue in the case of S '~ × S n, n > 3. Our point of departure is M. Gromov's metric on S 1 x S 3, and more general ex...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1997
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(96)00081-7