Abstract
We investigate hamiltonian properties of P m × C n, m ≥ 2 and even n ≥ 4, which is bipartite, in the presence of faulty vertices and/or edges. We show that P m × C n with n even is strongly hamiltonianlaceable if the number of faulty elements is one or less. When the number of faulty elements is two, it has a fault-free cycle of length at least mn−2 unless both faulty elements are contained in the same partite vertex set; otherwise, it has a fault-free cycle of length mn−4. A sufficient condition is derived for the graph with two faulty edges to have a hamiltonian cycle. By applying fault-hamiltonicity of P m × C n to a two-dimensional torus C m × C n, we obtain interesting hamiltonian properties of a faulty C m × C n.
This work was supported by grant No. 98-0102-07-01-3 from the Basic Research Program of the KOSEF.
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Park, JH., Kim, HC. (2003). Fault-Hamiltonicity of Product Graph of Path and Cycle. In: Warnow, T., Zhu, B. (eds) Computing and Combinatorics. COCOON 2003. Lecture Notes in Computer Science, vol 2697. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45071-8_33
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DOI: https://doi.org/10.1007/3-540-45071-8_33
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