Geodesic
Hamiltonian Paths in Distance Graphs
Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 904-916

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The object of study is the graph $$ G(n,r,s)=(V(n,r),E(n,r,s)) $$ with \begin{align*} V(n,r)=\{v : v \subset \{1,\dots,n\}, \, |v|=r\}, \\ E(n,r,s)=\{\{v,u\} : v,u \in V(n,r), \, |v \cap u|=s\}; \end{align*} i.e., the vertices of the graph are $r$-subsets of the set $\mathcal{R}_n=\{1,\dots,n\}$, and two vertices are connected by an edge if these vertices intersect in precisely $s$ elements. Two-sided estimates for the number of Hamiltonian paths in the graph $G(n,k,1)$ as $n \to \infty$ are obtained.
Keywords: distance graph, Hamiltonian path, simple path, hypergraph.
Mots-clés : clique 
@article{MZM_2015_97_6_a7,
     author = {V. V. Utkin},
     title = {Hamiltonian {Paths} in {Distance} {Graphs}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {904--916},
     publisher = {mathdoc},
     volume = {97},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a7/}
}
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V. V. Utkin. Hamiltonian Paths in Distance Graphs. Matematičeskie zametki, Tome 97 (2015) no. 6, pp. 904-916. http://geodesic.mathdoc.fr/item/MZM_2015_97_6_a7/