Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs re known to be NP-complete. Hover, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines. ,  will prove that the Hamiltonian cycle problem for supergrid graphs is NP-complete. It is easily derived from the Hamiltonian cycle result that the Hamiltonian path problem on supergrid graphs is also NP-complete.  then show that two subclasses of supergrid graphs, including rectangular (parallelism) and alphabet, always contain Hamiltonian cycles.
['Ruo-Wei Hung', 'Chih-Chia Yao', 'Shang-Ju Chan']
I am writing a research paper on a idea The Hamiltonian properties of supergrid graphs
[{"from": "human", "value": "I am writing a research paper on a idea The Hamiltonian properties of supergrid graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  first introduce a novel class of graphs, namely supergrid. Supergrid graphs include grid graphs and triangular grid graphs as their subgraphs. The Hamiltonian cycle and path problems for grid graphs and triangular grid graphs re known to be NP-complete. Hover, they are unknown for supergrid graphs. The Hamiltonian cycle (path) problem on supergrid graphs can be applied to control the stitching traces of computerized sewing machines. ,  will prove that the Hamiltonian cycle problem for supergrid graphs is NP-complete. It is easily derived from the Hamiltonian cycle result that the Hamiltonian path problem on supergrid graphs is also NP-complete.  then show that two subclasses of supergrid graphs, including rectangular (parallelism) and alphabet, always contain Hamiltonian cycles."}]