  Geographic routing is an appealing routing strategy that uses the location
information of the nodes to route the data. This technique uses only local
information of the communication graph topology and does not require
computational effort to build routing table or equivalent data structures. A
particularly efficient implementation of this paradigm is greedy routing, where
along the data path the nodes forward the data to a neighboring node that is
closer to the destination. The decreasing distance to the destination implies
the success of the routing scheme. A related problem is to consider an abstract
graph and decide whether there exists an embedding of the graph in a metric
space, called a greedy embedding, such that greedy routing guarantees the
delivery of the data. In the present paper, we use a metric-free definition of
greedy path and we show that greedy routing is successful on planar
triangulations without considering the existence of greedy embedding. Our
algorithm rely entirely on the combinatorial description of the graph structure
and the coordinate system requires O(log(n)) bits where n is the number of
nodes in the graph. Previous works on greedy routing make use of the embedding
to route the data. In particular, in our framework, it is known that there
exists an embedding of planar triangulations such that greedy routing
guarantees the delivery of data. The result presented in this article leads to
the question whether the success of (any) greedy routing strategy is always
coupled with the existence of a greedy embedding?
