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On open Hamiltonian walks in graphs. (English) Zbl 0758.05067
Summary: If $$G$$ is a graph of order $$n$$, an open Hamiltonian walk is meant any open sequence of edges of minimal length which includes every vertex of $$G$$. Clearly, the length of such an open walk is at least $$n-1$$, and is equal to $$n-1$$ if and only if $$G$$ contains a Hamiltonian path. In this paper, basic properties of open Hamiltonian walks and upper bounds of their lengths in some classes of graphs are studied.

##### MSC:
 05C45 Eulerian and Hamiltonian graphs
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