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Mat. Zametki, 2015, Volume 97, Issue 6, Pages 904–916 (Mi mz10557)  

Hamiltonian Paths in Distance Graphs

V. V. Utkin

Lomonosov Moscow State University

Abstract: 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,…,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 $\mathcal{R}_n=\{1,…,n\}$, 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, clique, hypergraph.

Funding Agency Grant Number
Russian Foundation for Basic Research 15-01-03530
This work was supported by the Russian Foundation for Basic Research (grant no. 15-01-03530).


DOI: https://doi.org/10.4213/mzm10557

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English version:
Mathematical Notes, 2015, 97:6, 919–929

Bibliographic databases:

Document Type: Article
UDC: 519.17
Received: 31.05.2014
Revised: 10.12.2014

Citation: V. V. Utkin, “Hamiltonian Paths in Distance Graphs”, Mat. Zametki, 97:6 (2015), 904–916; Math. Notes, 97:6 (2015), 919–929

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