4-Labelings and grid embeddings of plane quadrangulations

Authors:
Lali Barrière;Clemens Huemer
Affiliations:
Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya;Departament de Matemàtica Aplicada IV, Universitat Politècnica de Catalunya
Venue:
GD'09 Proceedings of the 17th international conference on Graph Drawing
Year:
2009

Citing 3
Cited 1

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Abstract

Finding aesthetic drawings of planar graphs is a main issue in graph drawing. Of special interest are rectangle of influence drawings.The graphs considered here are quadrangulations, that is, planar graphs all whose faces have degree four.We show that each quadrangulation on n vertices has a closed rectangle of influence drawing on the (n - 2) × (n - 2) grid. Biedl, Bretscher and Meijer [2] proved that every planar graph on n vertices without separating triangle has a closed rectangle of influence drawing on the (n - 1) × (n - 1) grid.Our method, which is completely different from that of [2], is in analogy to Schnyder's algorithm for embedding triangulations on an integer grid [9] and gives a simple algorithm.