Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  address graph decomposition problems that help the hybrid visualization of large#R##N#graphs, where different graphic metaphors (node-link, matrix, etc.) are used in the same#R##N#picture.  generalize the $X$-graphs of $Y$-graphs model introduced by Brandenburg#R##N#(Brandenburg, F.J.: Graph clustering I: Cycles of cliques. In Di Battista, G., #R##N#ed.: Graph Drawing (Proc. GD '97). Volume 1353 of Lecture Notes Comput. Sci., Springer-Verlag#R##N#(1997) 158--168) to formalize the problem of automatically identifying dense subgraphs#R##N#($Y$-graphs, clusters) that are prone to be collapsed and shown with a matricial#R##N#representation when needed.  show that (planar, $K_5$)-recognition, that is, the#R##N#problem of identifying $K_5$ subgraphs such that the graph obtained by collapsing them#R##N#is planar, is NP-hard. On the positive side,  show that it is possible to determine the#R##N#highest value of $k$ such that $G$ is a (planar,$k$-core)-graph in $O(m + n log(n))$ time.
['Vladimir Batagelj', 'Franz J. Brandenburg', 'Walter Didimo', 'Giuseppe Liotta', 'Maurizio Patrignani']
I am writing a research paper on a idea 08191 Working Group Report - X-graphs of Y-graphs and their Representations.
[{"from": "human", "value": "I am writing a research paper on a idea 08191 Working Group Report - X-graphs of Y-graphs and their Representations."}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  address graph decomposition problems that help the hybrid visualization of large#R##N#graphs, where different graphic metaphors (node-link, matrix, etc.) are used in the same#R##N#picture.  generalize the $X$-graphs of $Y$-graphs model introduced by Brandenburg#R##N#(Brandenburg, F.J.: Graph clustering I: Cycles of cliques. In Di Battista, G., #R##N#ed.: Graph Drawing (Proc. GD '97). Volume 1353 of Lecture Notes Comput. Sci., Springer-Verlag#R##N#(1997) 158--168) to formalize the problem of automatically identifying dense subgraphs#R##N#($Y$-graphs, clusters) that are prone to be collapsed and shown with a matricial#R##N#representation when needed.  show that (planar, $K_5$)-recognition, that is, the#R##N#problem of identifying $K_5$ subgraphs such that the graph obtained by collapsing them#R##N#is planar, is NP-hard. On the positive side,  show that it is possible to determine the#R##N#highest value of $k$ such that $G$ is a (planar,$k$-core)-graph in $O(m + n log(n))$ time."}]