an:00095322
Zbl 0758.05067
Vacek, Pavel
On open Hamiltonian walks in graphs
EN
Arch. Math., Brno 27a, 105-111 (1991).
0044-8753 1212-5059
1991
j
05C45
Hamiltonian graph; Hamiltonian path; Hamiltonian walk; open Hamiltonian walk; cactus
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.