On SelfApproaching and IncreasingChord Drawings of 3Connected Planar GraphsNöllenburg, Martin and Prutkin, Roman and Rutter, Ignaz (2014) On SelfApproaching and IncreasingChord Drawings of 3Connected Planar Graphs. In: Graph Drawing 22nd International Symposium, GD 2014, September 2426, 2014 , pp. 476487(Official URL: http://dx.doi.org/10.1007/9783662458037_40). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783662458037_40
AbstractAn stpath in a drawing of a graph is selfapproaching if during a traversal of the corresponding curve from s to any point t′ on the curve the distance to t′ is nonincreasing. A path has increasing chords if it is selfapproaching in both directions. A drawing is selfapproaching (increasingchord) if any pair of vertices is connected by a selfapproaching (increasingchord) path. We study selfapproaching and increasingchord drawings of triangulations and 3connected planar graphs. We show that in the Euclidean plane, triangulations admit increasingchord drawings, and for planar 3trees we can ensure planarity. Moreover, we give a binary cactus that does not admit a selfapproaching drawing. Finally, we show that 3connected planar graphs admit increasingchord drawings in the hyperbolic plane and characterize the trees that admit such drawings.
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