Prescribed matchings extend to Hamiltonian cycles in hypercubes with faulty edges
نویسندگان
چکیده
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 for n ≥ 2. Moreover, we can prove that when n ≥ 4 and M is nonempty this result still holds even if Qn has at most n− 1− ⌈ |M | 2 ⌉ faulty edges with one exception.
منابع مشابه
A note on fault-free mutually independent Hamiltonian cycles in hypercubes with faulty edges
In the paper “Fault-free Mutually Independent Hamiltonian Cycles in Hypercubes with Faulty Edges” (J. Comb. Optim. 13:153–162, 2007), the authors claimed that an n-dimensional hypercube can be embedded with (n−1−f )-mutually independent Hamiltonian cycles when f ≤ n−2 faulty edges may occur accidentally. However, there are two mistakes in their proof. In this paper, we give examples to explain ...
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عنوان ژورنال:
- Discrete Mathematics
دوره 321 شماره
صفحات -
تاریخ انتشار 2014