A Bramble like Witness for Large Branch-Width

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.

16 pages. This paper has been withdrawn by the author due to the main result already existing in the literature. The section on profiles may still be of interest