Combinatorics and Geometry of Finite and Infinite Squaregraphs

@article{Bandelt2010CombinatoricsAG,
  title={Combinatorics and Geometry of Finite and Infinite Squaregraphs},
  author={Hans-J{\"u}rgen Bandelt and Victor Chepoi and David Eppstein},
  journal={SIAM J. Discret. Math.},
  year={2010},
  volume={24},
  pages={1399-1440}
}
Squaregraphs were originally defined as finite plane graphs in which all inner faces are quadrilaterals (i.e., 4-cycles) and all inner vertices (i.e., the vertices not incident with the outer face) have degrees larger than three. The planar dual of a finite squaregraph is determined by a triangle-free chord diagram of the unit disk, which could alternatively be viewed as a triangle-free line arrangement in the hyperbolic plane. This representation carries over to infinite plane graphs with… 

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