Universal sets of n points for 1-bend drawings of planar graphs with n vertices

Authors:
Hazel Everett;Sylvain Lazard;Giuseppe Liotta;Stephen Wismath
Affiliations:
LORIA, INRIA Lorraine, Nancy Université, Nancy, France;LORIA, INRIA Lorraine, Nancy Université, Nancy, France;Dip. di Ingegneria Elettronica e dell'Informazione, Università degli Studi di Perugia;Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, Alberta, Canada
Venue:
GD'07 Proceedings of the 15th international conference on Graph drawing
Year:
2007

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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.