Excluding A Grid Minor In Planar Digraphs
Combinatorics
2015-10-05 v1 Discrete Mathematics
Abstract
In [Directed tree-width, J. Combin. Theory Ser. B 82 (2001), 138-154] we introduced the notion of tree-width of directed graphs and presented a conjecture, formulated during discussions with Noga Alon and Bruce Reed, stating that a digraph of huge tree-width has a large "cylindrical grid" minor. Here we prove the conjecture for planar digraphs, but many steps of the proof work in general. This is an unedited and unpolished manuscript from October 2001. Since many people asked for copies we are making it available in the hope that it may be useful. The conjecture was proved by Kawarabayashi and Kreutzer in arXiv:1411.5681.
Keywords
Cite
@article{arxiv.1510.00473,
title = {Excluding A Grid Minor In Planar Digraphs},
author = {Thor Johnson and Neil Robertson and Paul Seymour and Robin Thomas},
journal= {arXiv preprint arXiv:1510.00473},
year = {2015}
}
Comments
19 pages, no figures