eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-12-07
24:1
24:14
10.4230/LIPIcs.ISAAC.2017.24
article
Square-Contact Representations of Partial 2-Trees and Triconnected Simply-Nested Graphs
Da Lozzo, Giordano
Devanny, William E.
Eppstein, David
Johnson, Timothy
A square-contact representation of a planar graph G = (V,E) maps vertices in V to interior-disjoint axis-aligned squares in the plane and edges in E to adjacencies between the sides of the corresponding squares. In this paper, we study proper square-contact representations of planar graphs, in which any two squares are either disjoint or share infinitely many points.
We characterize the partial 2-trees and the triconnected cycle-trees allowing for such representations. For partial 2-trees our characterization uses a simple forbidden subgraph whose structure forces a separating triangle in any embedding. For the triconnected cycle-trees, a subclass of the triconnected simply-nested graphs, we use a new structural decomposition for the graphs in this family, which may be of independent interest. Finally, we study square-contact representations of general triconnected simply-nested graphs with respect to their outerplanarity index.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol092-isaac2017/LIPIcs.ISAAC.2017.24/LIPIcs.ISAAC.2017.24.pdf
Square-Contact Representations
Partial 2-Trees
Simply-Nested Graphs