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arXiv · 1312.4101

Trees and co-trees with constant maximum degree in planar 3-connected graphs

Therese Biedl
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Abstract

This paper considers the conjecture by Gr\"unbaum that every planar 3-connected graph has a spanning tree $T$ such that both $T$ and its co-tree have maximum degree at most 3. Here, the co-tree of $T$ 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 $T$ such that both $T$ and its co-tree have maximum degree at most 5. It can be found in linear time.

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Therese Biedl. 2013-12-15. Trees and co-trees with constant maximum degree in planar 3-connected graphs. https://arxiv.org/abs/1312.4101

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