On Planar Greedy Drawings of 3-Connected Planar Graphs
Giordano Da Lozzo, Anthony D'Angelo, Fabrizio Frati

TL;DR
This paper proves that every 3-connected planar graph has a planar greedy drawing, strengthening previous results and advancing towards the conjecture that such graphs can be drawn with convex faces for greedy routing.
Contribution
It establishes that all 3-connected planar graphs admit planar greedy drawings, an important step beyond earlier work and towards convex greedy embeddings.
Findings
Every 3-connected planar graph admits a planar greedy drawing.
This result strengthens previous theorems by Leighton and Moitra.
It serves as an intermediate step towards the convex greedy embedding conjecture.
Abstract
A graph drawing is if, for every ordered pair of vertices , there is a path from to such that the Euclidean distance to decreases monotonically at every vertex of the path. Greedy drawings support a simple geometric routing scheme, in which any node that has to send a packet to a destination "greedily" forwards the packet to any neighbor that is closer to the destination than itself, according to the Euclidean distance in the drawing. In a greedy drawing such a neighbor always exists and hence this routing scheme is guaranteed to succeed. In 2004 Papadimitriou and Ratajczak stated two conjectures related to greedy drawings. The states that every -connected planar graph admits a greedy drawing. The asserts that every -connected planar graph admits a planar…
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Advanced Graph Theory Research · Digital Image Processing Techniques
