Optimal Polygonal Representation of Planar Graphs

In this paper, we consider the problem of representing graphs by polygons whose sides touch. We show that at least six sides per polygon are necessary by constructing a class of planar graphs that cannot be represented by pentagons. We also show that the lower bound of six sides is matched by an upper bound of six sides with a linear time algorithm for representing any planar graph by touching hexagons. Moreover,

• Type: Conference
• Year: 2010
• Where: LATIN
• Authors: Emden R. Gansner, Yifan Hu, Michael Kaufmann, Stephen G. Kobourov
• Keywords: Information Retrieval, LATIN 2010, Linear Time Algorithm, Planar Graph, Polygon