Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem offinding a minimum-ight k-connected spanning subgraph ofa complete graph, assuming that the edge ights satisfy the triangle inequality, is studied. It is shown that the class ofminimum- ight k-edge connected spanning subgraphs can be restricted to those subgraphs which, in addition to the connectivity requirements, satisfy the following two conditions: (I) Every vertex has degree k or k + 1; (II) Removing any l, 2, ..-, or k edges does not leave the resulting connected components all k-edge connected. For the k-vertex connected case, the parallel result is obtained with "k-edge" replaced by "k-vertex," with the added technical restriction that V >= 2k for condition (I) to hold. This generalizes recent work ofMonma, Munson, and Pulleyblank for the case k 2.
['Daniel Bienstock', 'Ernest F. Brickell', 'Clyde L. Monma']
I am writing a research paper on a idea On the structure of minimum-weight k-connected spanning networks
[{"from": "human", "value": "I am writing a research paper on a idea On the structure of minimum-weight k-connected spanning networks"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: The problem offinding a minimum-ight k-connected spanning subgraph ofa complete graph, assuming that the edge ights satisfy the triangle inequality, is studied. It is shown that the class ofminimum- ight k-edge connected spanning subgraphs can be restricted to those subgraphs which, in addition to the connectivity requirements, satisfy the following two conditions: (I) Every vertex has degree k or k + 1; (II) Removing any l, 2, ..-, or k edges does not leave the resulting connected components all k-edge connected. For the k-vertex connected case, the parallel result is obtained with \"k-edge\" replaced by \"k-vertex,\" with the added technical restriction that V >= 2k for condition (I) to hold. This generalizes recent work ofMonma, Munson, and Pulleyblank for the case k 2."}]