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. 
@article{SEMR_2019_16_a79,
     author = {N. V. Prytkov and A. L. Perezhogin},
     title = {Hamiltonian connectivity of diagonal grid graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {2080--2089},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a79/}
}
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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/