Planar graphs are in 1-STRING

Authors:
J. Chalopin;D. Gonçalves;P. Ochem
Affiliations:
LaBRI, U.M.R., Université Bordeaux I, Talence Cedex, France;LaBRI, U.M.R., Université Bordeaux I, Talence Cedex, France;LaBRI, U.M.R., Université Bordeaux I, Talence Cedex, France
Venue:
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Year:
2007

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We prove that every planar graph is the intersection graph of strings in the plane, such that any two strings intersect at most once.