Trees and co-trees with constant maximum degree in planar 3-connected graphs
Discrete Mathematics
2013-12-17 v1 Combinatorics
Abstract
This paper considers the conjecture by Gr\"unbaum that every planar 3-connected graph has a spanning tree such that both and its co-tree have maximum degree at most 3. Here, the co-tree of is the spanning tree of the dual obtained by taking the duals of the non-tree edges. While Gr\"unbaum's conjecture remains open, we show that every planar 3-connected graph has a spanning tree such that both and its co-tree have maximum degree at most 5. It can be found in linear time.
Keywords
Cite
@article{arxiv.1312.4101,
title = {Trees and co-trees with constant maximum degree in planar 3-connected graphs},
author = {Therese Biedl},
journal= {arXiv preprint arXiv:1312.4101},
year = {2013}
}