Algebraic characterizations of outerplanar and planar graphs

Authors:
Hein van der Holst
Affiliations:
Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
Venue:
European Journal of Combinatorics
Year:
2007

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Abstract

A drawing of a graph in the plane is even if nonadjacent edges have an even number of intersections. Hanani's theorem characterizes planar graphs as those graphs that have an even drawing. In this paper we present an algebraic characterization of graphs that have an even drawing. Together with Hanani's theorem this yields an algebraic characterization of planar graphs. We will also present algebraic characterizations of subgraphs of paths, and of outerplanar graphs.