Geodesic
Paths of low weight in planar graphs
Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 121-135

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The existence of paths of low degree sum of their vertices in planar graphs is investigated. The main results of the paper are:
Keywords: planar graphs, polytopal graphs, paths, weight of an edge, weight of a path 
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     title = {Paths of low weight in planar graphs},
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Fabrici, Igor; Harant, Jochen; Jendrol', Stanislav. Paths of low weight in planar graphs. Discussiones Mathematicae. Graph Theory, Tome 28 (2008) no. 1, pp. 121-135. http://geodesic.mathdoc.fr/item/DMGT_2008_28_1_a8/