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A note on planar partial 3-trees

It implicitly follows from the work of [Colbourn, El-Mallah: On two dual classes of planar graphs. Discrete Mathematics 80(1): 21-40 (1990)] that every planar partial 3-tree is a subgraph of a planar 3-tree. This fact has already enabled to prove a couple of results for planar partial 3-trees by induction on the structure of the underlying planar 3-tree completion. We provide an explicit proof of this observation and strengthen it by showing that one can keep the plane drawing of the input graph unchanged.

preprint2012arXivOpen access
Jan KratochvílMichal Vaner
math.CODiscrete Mathematics
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Jan KratochvílMichal Vaner

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