Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose a conjecture regarding the lor bound for the number of edges in locally k-connected graphs and  prove it for $$k=2$$k=2. In particular,  show that every connected locally 2-connected graph is $$M_3$$M3-rigid. For the special case of surface triangulations, this fact was known before using topological methods.  generalize this result to all locally 2-connected graphs and give a purely combinatorial proof. Our motivation to study locally k-connected graphs comes from lor bound conjectures for flag triangulations of manifolds, and  discuss some more specific problems in this direction.
['Anna Adamaszek', 'Michal Adamaszek', 'Matthias Mnich', 'Jens M. Schmidt']
I am writing a research paper on a idea Lower Bounds for Locally Highly Connected Graphs
[{"from": "human", "value": "I am writing a research paper on a idea Lower Bounds for Locally Highly Connected Graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  propose a conjecture regarding the lor bound for the number of edges in locally k-connected graphs and  prove it for $$k=2$$k=2. In particular,  show that every connected locally 2-connected graph is $$M_3$$M3-rigid. For the special case of surface triangulations, this fact was known before using topological methods.  generalize this result to all locally 2-connected graphs and give a purely combinatorial proof. Our motivation to study locally k-connected graphs comes from lor bound conjectures for flag triangulations of manifolds, and  discuss some more specific problems in this direction."}]