A note on planar partial 3-trees
Discrete Mathematics
2012-10-31 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.1210.8113,
title = {A note on planar partial 3-trees},
author = {Jan Kratochvíl and Michal Vaner},
journal= {arXiv preprint arXiv:1210.8113},
year = {2012}
}
Comments
6 pages, 3 figures. To be published (not decided where yet)