Discussiones Mathematicae Graph Theory 27(3) (2007)
471-483
DOI: https://doi.org/10.7151/dmgt.1374
TOWARDS A CHARACTERIZATION OF BIPARTITE SWITCHING CLASSES BY MEANS OF FORBIDDEN SUBGRAPHS
Jurriaan Hage
Department of Information | Tero Harju
Department of Mathematics |
Abstract
We investigate which switching classes do not contain a bipartite graph. Our final aim is a characterization by means of a set of critically non-bipartite graphs: they do not have a bipartite switch, but every induced proper subgraph does. In addition to the odd cycles, we list a number of exceptional cases and prove that these are indeed critically non-bipartite. Finally, we give a number of structural results towards proving the fact that we have indeed found them all. The search for critically non-bipartite graphs was done using software written in C and Scheme. We report on our experiences in coping with the combinatorial explosion.Keywords: switching classes, bipartite graphs, forbidden subgraphs, combinatorial search.
2000 Mathematics Subject Classification: 05C22, 05C75.
References
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Received 19 May 2006
Revised 13 June 2007
Accepted 13 June 2007
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