Hamilton Circuits in Tree Graphs

• Published in: IEEE transactions on circuit theory Vol. 13; no. 1; pp. 82 - 90
• Main Author: Cummins, R.
• Format: Journal Article
• Language: English
• Published: IEEE 01-01-1966
• Subjects: Circuit theory; Marine vehicles; Tree graphs
• ISSN: 0018-9324; 2374-9555
• DOI: 10.1109/TCT.1966.1082546

Two operations for augmenting networks (linear graphs) are defined: edge insertion and vertex insertion. These operations are sufficient to allow the construction of arbitrary nonseparable networks, starting with a simple circuit. The tree graph of a network is defined as a linear graph in which each vertex corresponds to a tree of the network, and each edge corresponds to an elementary tree transformation between trees of the network. A property of tree graphs, referred to as "Property H," is defined: if t_{\alpha} and t_b are two trees of a network, and if t_{\alpha} and t_b are related by an elementary tree transformation, then there exists a Hamilton Circuit through the tree graph such that t_{\alpha} and t_b are adjacent in the circuit. It is shown that any tree graph containing more than two vertices has Property H.