A note on planar partial 3-trees

Abstract

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.

6 pages, 3 figures. To be published (not decided where yet)

References in corpus (1)

• The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree

Cited by in corpus (6)

• The Planar Slope Number of Planar Partial 3-Trees of Bounded Degree
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• Universality in minor-closed graph classes
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• SEFE with No Mapping via Large Induced Outerplane Graphs in Plane Graphs