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- W4287113669 abstract "A graph is emph{hamiltonian-connected} if every pair of vertices can be connected by a hamiltonian path, and it is emph{hamiltonian} if it contains a hamiltonian cycle. Every hamiltonian-connected graph is hamiltonian, however we also construct families of nonhamiltonian graphs with `many' hamiltonian paths, where 'many' is interpreted with respect to the number of pairs of vertices connected by hamiltonian paths. We then consider minimal graphs that are hamiltonian-connected; we show that any order-$n$ graph that is hamiltonian-connected graphs must have $geq 3n/2$ edges, and we construct an infinite family of graphs realizing this minimum." @default.
- W4287113669 created "2022-07-25" @default.
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- W4287113669 date "2021-06-24" @default.
- W4287113669 modified "2023-09-24" @default.
- W4287113669 title "Graphs with Many Hamiltonian Paths" @default.
- W4287113669 doi "https://doi.org/10.48550/arxiv.2106.13372" @default.
- W4287113669 hasPublicationYear "2021" @default.
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