 
Summary: Cartesian products of graphs as subgraphs of
de Bruijn graphs of dimension at least three
Thomas Andreae a , Martin Hintz a , Michael N¨olle b , Gerald Schreiber b , Gerald W.
Schuster a , Hajo Seng a
a Universit¨at Hamburg, Mathematisches Seminar, Bundesstraße 55, D20146 Hamburg,
Germany
b Technische Universit¨at HamburgHarburg, Technische Informatik I, Harburger Schloß
straße 20, D21071 Hamburg, Germany
4th Twente Workshop on graphs and combinatorial optimization, Twente,
NL, June, 1995. Accepted for publication in ``Discrete Applied
Mathematics''.
Abstract
Given a Cartesian product G = G 1 \Theta : : : \Theta Gm (m – 2) of nontrivial connected
graphs G i and the base d, dimension D de Bruijn graph B(d; D), it is inves
tigated under which conditions G is (or is not) a subgraph of B(d; D). We
present a complete solution of this problem for the case D – 4. For D = 3, we
give partial results including a complete solution for the case that G is a torus,
i.e., G is the Cartesian product of cycles.
Key words: de Bruijn graphs, Cartesian products of graphs, interconnection networks,
subgraph embeddings, hypercubes, tori, parallel and distributed computing
