Twin Bob Plan Composition of Stedman Triples: Partitioning of Graphs into Hamiltonian Subgraphs


Deryn Griffiths


Research Report 94-37
Date: 7 Nov 1994


This paper considers finite directed graphs with in-degree 2 and out-degree 2 and uses the fact that every edge belongs to a unique alternating 2n-gon

for some n.

A covering of a directed graph is a collection of disjoint directed circuits which together use each vertex of the graph exactly once. Thus a covering partitions the vertices of a graph, each associated subgraph being Hamiltonian.

The paper shows how to transform one covering into a new one. Each step of the transformation involves all the edges of an alternating 2n-gon. It is shown how the parity of the number of circuits in the covering at each step changes or not according to the parity of n.

This result is applied to bell-ringing and it is shown that there is no Twin-Bob extent of Stedman Triples.

Key phrases

campanology. Stedman Triples. Hamiltonian directed graphs.

AMS Subject Classification (1991)

Primary: 05C90
Secondary: 05C20, 05C25, 05C45


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