Characterizing Planarity by the Splittable Deque

  • Christopher Auer
  • Franz J. Brandenburg
  • Andreas Gleißner
  • Kathrin Hanauer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8242)

Abstract

A graph layout describes the processing of a graph G by a data structure \(\mathcal{D}\), and the graph is called a \(\mathcal{D}\)-graph. The vertices of G are totally ordered in a linear layout and the edges are stored and organized in \(\mathcal{D}\). At each vertex, all edges to predecessors in the linear layout are removed and all edges to successors are inserted. There are intriguing relationships between well-known data structures and classes of planar graphs: The stack graphs are the outerplanar graphs [4], the queue graphs are the arched leveled-planar graphs [12], the 2-stack graphs are the subgraphs of planar graphs with a Hamilton cycle [4], and the deque graphs are the subgraphs of planar graphs with a Hamilton path [2]. All of these are proper subclasses of the planar graphs, even for maximal planar graphs.

We introduce splittable deques as a data structure to capture planarity. A splittable deque is a deque which can be split into sub-deques. The splittable deque provides a new insight into planarity testing by a game on switching trains. Here, we use it for a linear-time planarity test of a given rotation system.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Christopher Auer
    • 1
  • Franz J. Brandenburg
    • 1
  • Andreas Gleißner
    • 1
  • Kathrin Hanauer
    • 1
  1. 1.University of PassauGermany

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