Hamiltonian paths and Hamiltonian cycles passing through prescribed linear forests in star graph with fault-tolerant edges
In this paper, we focus on Hamiltonian paths and Hamiltonian cycles passing through prescribed linear forests in n-dimensional star graph Sn with fault-tolerant edges. Let F⊆E(Sn) be a fault-tolerant edges set and L be a linear forest of Sn−F, and |E(L)|+|F|≤n−3. For any two vertices u and v in diff...
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Published in | Discrete Applied Mathematics Vol. 334; pp. 68 - 80 |
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Main Authors | , , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
31.07.2023
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Subjects | |
Online Access | Get full text |
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Summary: | In this paper, we focus on Hamiltonian paths and Hamiltonian cycles passing through prescribed linear forests in n-dimensional star graph Sn with fault-tolerant edges. Let F⊆E(Sn) be a fault-tolerant edges set and L be a linear forest of Sn−F, and |E(L)|+|F|≤n−3. For any two vertices u and v in different partite sets, we prove that if {u,v} and L are compatible in Sn, then there is a Hamiltonian path of Sn−F between u and v, which passes through each edge of L. That is, Sn is (n−3)-edge fault-tolerant prescribed Hamiltonian laceable for n≥4. And we show that there is a Hamiltonian cycle of Sn−F passing through each edge of L, that is, Sn is (n−3)-edge fault-tolerant prescribed Hamiltonian for n≥4. These results are optimal in the described sense. |
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ISSN: | 0166-218X 1872-6771 |
DOI: | 10.1016/j.dam.2023.02.016 |