Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph G is akly 4-connected if it is 3-connected, has at least ve vertices, and for every pair (A;B) such that A[B = V (G),jA\Bj = 3 and no edge has one end in A B and the other in B A, one of the induced subgraphs G[A];G[B] has at most four edges.  describe a set of constructions that starting from a akly 4-connected planar graph G produce a nite list of non-planar akly 4-connected graphs, each having a minor isomorphic to G, such that every non-planar akly 4-connected graph H that has a minor isomorphic to G has a minor isomorphic to one of the graphs in the list. Our main result is more general and applies in particular to polyhedral embeddings in any surface.
['Rajneesh Hegde', 'Robin Thomas']
I am writing a research paper on a idea Non-Embeddable Extensions of Embedded Minors
[{"from": "human", "value": "I am writing a research paper on a idea Non-Embeddable Extensions of Embedded Minors"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A graph G is akly 4-connected if it is 3-connected, has at least ve vertices, and for every pair (A;B) such that A[B = V (G),jA\\Bj = 3 and no edge has one end in A B and the other in B A, one of the induced subgraphs G[A];G[B] has at most four edges.  describe a set of constructions that starting from a akly 4-connected planar graph G produce a nite list of non-planar akly 4-connected graphs, each having a minor isomorphic to G, such that every non-planar akly 4-connected graph H that has a minor isomorphic to G has a minor isomorphic to one of the graphs in the list. Our main result is more general and applies in particular to polyhedral embeddings in any surface."}]