Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   The structure of certain non-2-extendable planar graphs is studied first. In particular, 4-connected 5-regular planar graphs which are not 2-extendable are investigated and examples of these are presented. It is then proved that all 5-connected even planar graphs are 2-extendable. Finally, a certain configuration called a  generalized butterfly  is defined and it is shown that 4-connected maximal planar even graphs which contain no generalized butterfly are 2-extendable.
['Michael D. Plummer']
I am writing a research paper on a idea Extending matchings in planar graphs IV
[{"from": "human", "value": "I am writing a research paper on a idea Extending matchings in planar graphs IV"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Abstract   The structure of certain non-2-extendable planar graphs is studied first. In particular, 4-connected 5-regular planar graphs which are not 2-extendable are investigated and examples of these are presented. It is then proved that all 5-connected even planar graphs are 2-extendable. Finally, a certain configuration called a  generalized butterfly  is defined and it is shown that 4-connected maximal planar even graphs which contain no generalized butterfly are 2-extendable."}]