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Received 8 February 2005
Revised 14 August 2005
Discussiones Mathematicae Graph Theory 26(2) (2006)
343-349
DOI: https://doi.org/10.7151/dmgt.1325
ORTHOGONAL DOUBLE COVERS OF COMPLETE GRAPHS BY FAT CATERPILLARS
| Dalibor Froncek
Department of Mathematics and Statistics | Uwe Leck
Institut für Mathematik, Universität Rostock |
Abstract
An orthogonal double cover (ODC) of the complete graph Kn by some graph G is a collection of n spanning subgraphs of Kn, all isomorphic to G, such that any two of the subgraphs share exactly one edge and every edge of Kn is contained in exactly two of the subgraphs. A necessary condition for such an ODC to exist is that G has exactly n−1 edges. We show that for any given positive integer d, almost all caterpillars of diameter d admit an ODC of the corresponding complete graph.Keywords: ODC, orthogonal double cover, graph decomposition, self-orthogonal factorization.
2000 Mathematics Subject Classification: 05B40, 05C70.
References
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Revised 14 August 2005
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