Discussiones Mathematicae Graph Theory 27(3) (2007) 471-483
doi: 10.7151/dmgt.1374

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Jurriaan Hage

Department of Information
and Computing Sciences, University Utrecht
P.O. Box 80.089, 3508 TB Utrecht, Netherlands
e-mail: jur@cs.uu.nl

Tero Harju

Department of Mathematics
University of Turku
FIN-20014 Turku, Finland


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.


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Received 19 May 2006
Revised 13 June 2007
Accepted 13 June 2007