Geodesic
Hamiltonian Extendable Graphs
Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 843-859

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A graph is called Hamiltonian extendable if there exists a Hamiltonian path between any two nonadjacent vertices. In this paper, we give an explicit formula of the minimum number of edges for Hamiltonian extendable graphs and we also characterize the degree sequence for Hamiltonian extendable graphs with minimum number of edges. Besides, we completely characterize the pairs of forbidden subgraphs for 2-connected graphs to be Hamiltonian extendable.
Keywords: Hamiltonian extendable, forbidden subgraph 
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     author = {Yang, Xiaojing and Xiong, Liming},
     title = {Hamiltonian {Extendable} {Graphs}},
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Yang, Xiaojing; Xiong, Liming. Hamiltonian Extendable Graphs. Discussiones Mathematicae. Graph Theory, Tome 42 (2022) no. 3, pp. 843-859. http://geodesic.mathdoc.fr/item/DMGT_2022_42_3_a10/