Matchings extend to Hamiltonian cycles in 5-cube
نویسندگان
چکیده
منابع مشابه
Prescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges
Ruskey and Savage asked the following question: Does every matching of Qn for n ≥ 2 extend to a Hamiltonian cycle of Qn? J. Fink showed that the question is true for every perfect matching, and solved the Kreweras’ conjecture. In this paper we consider the question in hypercubes with faulty edges. We show that every matching M of at most 2n− 1 edges can be extended to a Hamiltonian cycle of Qn ...
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Kreweras’ conjecture [1] asserts that any perfect matching of the hypercube Qd, d ≥ 2, can be extended to a Hamilton cycle. We prove this conjecture.
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Ruskey and Savage in 1993 asked whether every matching in a hypercube can be extended to a Hamiltonian cycle. A positive answer is known for perfect matchings, but the general case has been resolved only for matchings of linear size. In this paper we show that there is a quadratic function q(n) such that every matching in the n-dimensional hypercube of size at most q(n) may be extended to a cyc...
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ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2018
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2010