Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The semidefinite programming formulation of the Lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number χ(G) or the clique number ω(G) of a graph, but also leads to heuristics for graph coloring and extracting large cliques. This semidefinite programming formulation can be tightened toward either χ(G) or ω(G) by adding several types of cutting planes.  explore several such strengthenings, and show that some of them can be computed with the same effort as the theta number.  also investigate computational simplifications for graphs with rich automorphism groups.
['Igor Dukanovic', 'Franz Rendl']
I am writing a research paper on a idea Semidefinite programming relaxations for graph coloring and maximal clique problems
[{"from": "human", "value": "I am writing a research paper on a idea Semidefinite programming relaxations for graph coloring and maximal clique problems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The semidefinite programming formulation of the Lovasz theta number does not only give one of the best polynomial simultaneous bounds on the chromatic number \u03c7(G) or the clique number \u03c9(G) of a graph, but also leads to heuristics for graph coloring and extracting large cliques. This semidefinite programming formulation can be tightened toward either \u03c7(G) or \u03c9(G) by adding several types of cutting planes.  explore several such strengthenings, and show that some of them can be computed with the same effort as the theta number.  also investigate computational simplifications for graphs with rich automorphism groups."}]