Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  shall prove that any two graphs G1 and G2 can be embedded together on a closed surface of genus g with at most 4g · β(G1) · β(G2) crossing points on their edges if they are embeddable on the surface, where β(G) stands for the Betti number of G, and show several observations on crossings of graph embedding pairs. © 2000 John Wiley & Sons, Inc. J Graph Theory 36: 8–23, 2001
['Seiya Negami']
I am writing a research paper on a idea Crossing numbers of graph embedding pairs on closed surfaces
[{"from": "human", "value": "I am writing a research paper on a idea Crossing numbers of graph embedding pairs on closed surfaces"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  shall prove that any two graphs G1 and G2 can be embedded together on a closed surface of genus g with at most 4g\u2009\u00b7\u2009\u03b2(G1)\u2009\u00b7\u2009\u03b2(G2) crossing points on their edges if they are embeddable on the surface, where \u03b2(G) stands for the Betti number of G, and show several observations on crossings of graph embedding pairs. \u00a9 2000 John Wiley & Sons, Inc. J Graph Theory 36: 8\u201323, 2001"}]