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3-Trees in polyhedral maps

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Abstract

We show that the vertices of the graph of any polyhedral map on the projective plane, torus or Klein bottle can be covered by a subgraph that is a tree of maximum valence 3. This extends a theorem of the author, who previously proved this theorem for the graphs of 3-dimensional polytopes. Several theorems dealing with paths in polyhedral maps are a consequence of these theorems.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of California, 95616-8633, Davis, CA, USA

    D. W. Barnette

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  1. D. W. Barnette
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Barnette, D.W. 3-Trees in polyhedral maps. Israel J. Math. 79, 251–256 (1992). https://doi.org/10.1007/BF02808218

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  • DOI: https://doi.org/10.1007/BF02808218

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