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Towards a characterization of bipartite switching classes by means of forbidden subgraphs

Jurriaan HageTero Harju — 2007

Discussiones Mathematicae Graph Theory

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...

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