Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the Lovasz number v along with two further SDP relaxations v 1/2 , v 2  of the independence number and the corresponding relaxations v, v 1/2 , v 2  of the chromatic number on random graphs G n,p .  prove that v, v 1/2 , v 2 (G n,p ) in the case p < n -1/2-e  are concentrated in intervals of constant length. Moreover,  estimate the probable value of v, v(G n,p ) etc. for essentially the entire range of edge probabilities p. As applications,  give improved algorithms for approximating α(G n,p ) and for deciding k-colorability in polynomial expected time.
['Amin Coja-Oghlan']
I am writing a research paper on a idea The Lovász Number of Random Graphs.
[{"from": "human", "value": "I am writing a research paper on a idea The Lov\u00e1sz Number of Random Graphs."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the Lovasz number v along with two further SDP relaxations v 1/2 , v 2  of the independence number and the corresponding relaxations v, v 1/2 , v 2  of the chromatic number on random graphs G n,p .  prove that v, v 1/2 , v 2 (G n,p ) in the case p < n -1/2-e  are concentrated in intervals of constant length. Moreover,  estimate the probable value of v, v(G n,p ) etc. for essentially the entire range of edge probabilities p. As applications,  give improved algorithms for approximating \u03b1(G n,p ) and for deciding k-colorability in polynomial expected time."}]