Universal Sets of n Points for One-bend Drawings of Planar Graphs with n Vertices

Authors:
Hazel Everett;Sylvain Lazard;Giuseppe Liotta;Stephen Wismath
Affiliations:
Université Nancy 2, LORIA, INRIA Nancy Grand Est, Nancy, France;Université Nancy 2, LORIA, INRIA Nancy Grand Est, Nancy, France;Università degli Studi di Perugia, Dip. di Ingegneria Elettronica e dell’Informazione, Perugia, Italy;University of Lethbridge, Department of Mathematics and Computer Science, Lethbridge, Alberta, Canada
Venue:
Discrete & Computational Geometry
Year:
2010

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Abstract

This paper shows that any planar graph with n vertices can be point-set embedded with at most one bend per edge on a universal set of n points in the plane. An implication of this result is that any number of planar graphs admit a simultaneous embedding without mapping with at most one bend per edge.