Fault-Free Hamiltonian Cycles in Balanced Hypercubes with Conditional Edge Faults
2019 ◽
Vol 30
(05)
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pp. 693-717
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Keyword(s):
The balanced hypercube, [Formula: see text], is a variant of hypercube [Formula: see text]. Zhou et al. [Inform. Sci. 300 (2015) 20–27] proposed an interesting problem that whether there is a fault-free Hamiltonian cycle in [Formula: see text] with each vertex incident to at least two fault-free edges. In this paper, we consider this problem and show that each fault-free edge lies on a fault-free Hamiltonian cycle in [Formula: see text] after no more than [Formula: see text] faulty edges occur if each vertex is incident with at least two fault-free edges for all [Formula: see text]. Our result is optimal with respect to the maximum number of tolerated edge faults.
2007 ◽
Vol 08
(03)
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pp. 253-284
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2020 ◽
Vol 12
(03)
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pp. 2050036
Keyword(s):
1993 ◽
Vol 115
(2)
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pp. 208-213
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2011 ◽
Vol 471-472
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pp. 263-267
Keyword(s):
2012 ◽
Vol 21
(14)
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pp. 1250132
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Keyword(s):
2011 ◽
Vol 12
(04)
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pp. 337-343
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