Examples of using Counterexample in English and their translations into Russian
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Now Ubuntu GNU/Linux has become a counterexample.
A counterexample was proposed by Diestel and Leader in 2001.
In 2005, Eskin, Fisher, andWhyte confirmed the counterexample.
Show with a counterexample that the Hückel rule is not a necessary condition for aromaticity.
The ZetaGrid project was set up to search for a counterexample to the Riemann hypothesis.
Robinson(1979) characterized the combinations of k andthe dimension n that permit a counterexample.
A counterexample near 1018 would require a prime gap fifty million times the size of the average gap.
In Corollary 1.4 the arc I cannot be replaced by S1:the standard 3-winding is a counterexample 8.
Computational experiments have shown that, if a counterexample exists, it would have to have more than 177 vertices.
In the paper some necessary and sufficient conditions for this possibility are obtained and one counterexample is constructed.
In the other directions, Kelmans showed that a counterexample could be transformed into a counterexample to the original Barnette conjecture.
Although the truth of Barnette's conjecture remains unknown,computational experiments have shown that there is no counterexample with fewer than 86 vertices.
Published in 1973, it provides a counterexample to the Crispin Nash-Williams conjecture that every 4-regular 4-vertex-connected graph is Hamiltonian.
It is a small graph that serves as a useful example and counterexample for many problems in graph theory.
It can thus be used as a counterexample against the idea that every Artinian module is Noetherian whereas every Artinian ring is Noetherian.
Tait conjectured that all amphichiral knots had even crossing number, but a counterexample was found by Morwen Thistlethwaite et al. in 1998.
If a counterexample is being sought or a large-scale proof by exhaustion is being attempted, distributed computing techniques may be used to divide the calculations between multiple computers.
The Kittell graph is named after Irving Kittell,who used it as a counterexample to Alfred Kempe's flawed proof of the four-color theorem.
This publication marks the first known appearance of the Petersen graph in the mathematical literature,12 years before Julius Petersen's use of the same graph as a counterexample to an edge coloring problem.
A commentator who signed his name simply as"S" provided the counterexample of( e- 1/ t) t{\displaystyle\textstyle( e^{ -1/t})^{ t}}, and this quieted the debate for some time.
A minimally imperfect Berge graph cannot have any of these decompositions,from which it follows that no counterexample to the theorem can exist.
For k 8, this is not true: a graph found by Catlin(1979) as a counterexample to Hajós's conjecture that k-chromatic graphs contain a subdivision of Kk,also serves as a counterexample to this problem.
It was proposed by P. G. Tait(1884) and disproved by W. T. Tutte(1946),who constructed a counterexample with 25 faces, 69 edges and 46 vertices.
Therefore, if a counterexample to the Erdős-Straus conjecture exists, the smallest n forming a counterexample would have to be a prime number, and it can be further restricted to one of six infinite arithmetic progressions modulo 840.
In a classical CEGAR algorithm a path in a program to be explored is called a counterexample and it means a path to the error state.
As a finite connected vertex-transitive graph that contains no Hamiltonian cycle,the Coxeter graph is a counterexample to a variant of the Lovász conjecture, but the canonical formulation of the conjecture asks for an Hamiltonian path and is verified by the Coxeter graph.
David W. Barnette(1969) proposed a weakened combination of Tait's and Tutte's conjectures, stating that every bipartite cubic polyhedron is Hamiltonian,or, equivalently, that every counterexample to Tait's conjecture is non-bipartite.
It is known through computer searches of Gordon Royle andKlas Markström that any counterexample must have at least 17 vertices, and any cubic counterexample must have at least 30 vertices.
A stronger conjecture that the two numbers are always coprime was disproved by Stephens(1971) with the counterexample p 17 and q 3313 with common factor 2pq+ 1 112643.
As a finite connected vertex-transitive graph that does not have a Hamiltonian cycle,the Petersen graph is a counterexample to a variant of the Lovász conjecture, but the canonical formulation of the conjecture asks for a Hamiltonian path and is verified by the Petersen graph.