Abstract
This paper considers the conjecture by Grünbaum 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 Grünbaum’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.
Supported by NSERC and the Ross and Muriel Cheriton Fellowship. Research initiated while participating at Dagstuhl seminar 13421.
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Biedl, T. (2014). Trees and Co-trees with Bounded Degrees in Planar 3-connected Graphs. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_6
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DOI: https://doi.org/10.1007/978-3-319-08404-6_6
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