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On Hamiltonian cycles and Hamiltonian paths. (English) Zbl 1182.68142
Summary: A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths. The significance of the theorems is discussed, and it is shown that the famous Ore’s theorem directly follows from our result.

68R05 Combinatorics in computer science
68R10 Graph theory (including graph drawing) in computer science
Full Text: DOI
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