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- W2024832813 abstract "A graph G is n -hamiltonian (resp. n -edge hamiltonian) if after the removal of any k vertices (resp. edges) with 0⩽ k ⩽ n , the resulting graph is hamiltonian. The k th power of a graph G is the graph having the same vertex-set as G and such that u and υ , vertices of G k , are adjacent if and only if the distance between u and υ in G is at most k . In this paper, we prove that if G is a connected graph then G k is ( k −2)-edge hamiltonian if k ⩾3 and | V ( G )| k +1. Furthermore, if G is 2-connected and | V ( G )| k +2 then G k is ( k −1)-edge hamiltonian." @default.
- W2024832813 created "2016-06-24" @default.
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- W2024832813 date "1984-01-01" @default.
- W2024832813 modified "2023-09-25" @default.
- W2024832813 title "Powers of connected graphs and hamiltonicity" @default.
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- W2024832813 doi "https://doi.org/10.1016/0012-365x(84)90106-7" @default.
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