How to get L1,L2,L3categories based on brand?

We have a requirement like a user inputs a brand name(ManufacturerName) in backoffice we have to show its specific category structure. like we are having

Root Category->Home Appliances(L1)->Refrigerators(L2)->Frost Refrigerator(L3)->De-frost(L3)

products tagged under L3 are having manufacturer Names i.e brands. Now if I input a manufacturer name how to get its category structure and display ?