Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The class of fork-free graphs is an extension of claw-free graphs and their subclass of line graphs. The first polynomial-time solution to the maximum ight independent set problem in the class of line graphs, which is equivalent to the maximum matching problem in general graphs, has been proposed by Edmonds in 1965 and then extended to the entire class of claw-free graphs by Minty in 1980. Recently, Alekseev proposed a solution for the larger class of fork-free graphs, but only for the unighted version of the problem, i.e. finding an independent set of maximum cardinality. In the present paper,  describe the first polynomial-time algorithm to solve the problem for ighted fork-free graphs.
['Vadim V. Lozin', 'Martin Milanič']
I am writing a research paper on a idea A polynomial algorithm to find an independent set of maximum weight in a fork-free graph
[{"from": "human", "value": "I am writing a research paper on a idea A polynomial algorithm to find an independent set of maximum weight in a fork-free graph"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The class of fork-free graphs is an extension of claw-free graphs and their subclass of line graphs. The first polynomial-time solution to the maximum ight independent set problem in the class of line graphs, which is equivalent to the maximum matching problem in general graphs, has been proposed by Edmonds in 1965 and then extended to the entire class of claw-free graphs by Minty in 1980. Recently, Alekseev proposed a solution for the larger class of fork-free graphs, but only for the unighted version of the problem, i.e. finding an independent set of maximum cardinality. In the present paper,  describe the first polynomial-time algorithm to solve the problem for ighted fork-free graphs."}]