Geodesic
Long induced paths in 3-connected planar graphs
Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 105-107

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It is shown that every 3-connected planar graph with a large number of vertices has a long induced path.
Keywords: induced paths, 3-connected planar graphs 
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Arocha, Jorge; Valencia, Pilar. Long induced paths in 3-connected planar graphs. Discussiones Mathematicae. Graph Theory, Tome 20 (2000) no. 1, pp. 105-107. http://geodesic.mathdoc.fr/item/DMGT_2000_20_1_a7/