Geodesic
Hamiltonian connectivity of diagonal grid graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 2080-2089.

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A graph $G$ is called Hamiltonian connected graph if for every pair of distinct vertices $u, v \in V(G)$ there exists a hamiltonian $(u,v)$-path in $G$. In this paper we prove Hamiltonian connectivity of the family of infinite two-dimensional diagonal grid induced subgraphs with added horizontal and vertical border edges. A generalization for multidimensional case is given. These results are applied to prove the existence of discrete dynamic systems with arbitrary control functions with some given functioning properties.
Keywords: hamiltonian connectivity, grid graph, discrete dynamic system. 
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N. V. Prytkov; A. L. Perezhogin. Hamiltonian connectivity of diagonal grid graphs. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 2080-2089. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a79/

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