Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let G be a graph and f : V(G) → {1, 3, 5,...}. Then a subgraph H of G is called a (1, f)-odd subgraph if degH(x) ∈ {1,3, ..., f(x)} for all x ∈ V(H). If f(x) = 1 for all x ∈ V(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K| > |H|.  show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular,  give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching.
['Mikio Kano', 'Gyula Y. Katona']
I am writing a research paper on a idea Odd subgraphs and matchings
[{"from": "human", "value": "I am writing a research paper on a idea Odd subgraphs and matchings"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Let G be a graph and f : V(G) \u2192 {1, 3, 5,...}. Then a subgraph H of G is called a (1, f)-odd subgraph if degH(x) \u2208 {1,3, ..., f(x)} for all x \u2208 V(H). If f(x) = 1 for all x \u2208 V(G), then a (1,f)-odd subgraph is nothing but a matching. A (1,f)-odd subgraph H of G is said to be maximum if G has no (1,f)-odd subgraph K such that |K| > |H|.  show that (1,f)-odd subgraphs have some properties similar to those of matchings, in particular,  give a formula for the order of a maximum (1,f)-odd subgraph, which is similar to that for the order of a maximum matching."}]