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

## Author

**Deryn Griffiths**

## Status

Research Report 94-37

Date: 7 Nov 1994

## Abstract

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

## Content

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- PostScript:
- 2bob-sted.ps.gz (51kB) or
2bob-sted.ps (208kB)

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Sydney Mathematics and Statistics