 Every polyhedral graph has a Christmas cactus subgraph that includes all of its vertices, a fact that plays an essential role in a proof by that every polyhedral graph has a greedy embedding in the Euclidean plane, an assignment of coordinates to the vertices for which greedy forwarding succeeds in routing messages between all pairs of vertices.In topological graph theory, the graphs whose cellular embeddings are all planar are exactly the subfamily of the cactus graphs with the additional property that each vertex belongs to at most one cycle.These graphs have two forbidden minors, the diamond graph and the five-vertex friendship graph.