A Bramble like Witness for Large Branch-Width

preprint2015arXivOpen access

Abstract

Using the new framework of graph separations developed recently by Diestel and Oum, we show that there is a natural witness to large branch-width which can be defined in a similar way to a bramble. We also apply our methods to a more recent object of study in the area, a common generalization of tangles and blocks, called profiles.

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