2 research outputs found

    Restricted 2-factors in bipartite graphs

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    The k-restricted 2-factor problem is that of finding a spanning subgraph consisting of disjoint cycles with no cycle of length less than or equal to k. It is a generalization of the well known Hamilton cycle problem and is equivalent to this problem when n2≤k≤n-1 . This paper considers necessary and sufficient conditions, algorithms, and polyhedral conditions for 2-factors in bipartite graphs and restricted 2-factors in bipartite graphs. We introduce a generalization of the necessary and sufficient condition for 4-restricted 2-factors in bipartite graphs to 2k-restricted 2-factors in bipartite graphs of a particular form

    Programming the nanocell, a random array of molecules

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    The emerging field of molecular electronics seeks to create computational function from individual molecules or arrays of molecules. These nanoscale devices would then enable the production of faster, denser, cheaper computers. Clearly, there are many obstacles to building such devices, one of which is to develop methods for using lithographic wires to address molecules that are many orders of magnitude smaller in size. In this thesis, a moletronics design is presented that offers a method for connecting nanometer molecules to the world-at-large. This architecture involves the production of nanocells, or random arrays of molecules and metallic nanoparticles. The molecules have two discrete states and exhibit electrical behavior that enables complex logic in a nanocell. Methods are presented to take a random array of such switch states and alter them to program a nanocell as a useful logical device. Simulations of this programming process are presented and show that it is theoretically possible to obtain very high level function from these cells. Observations made during simulations are then used to formulate theorems about the programmability of nanocells. These theorems demonstrate that there is a dense solution space of molecular switch states that give rise to certain computation within a nanocell. Future directions of research, such as methods for wiring multiple nanocells together, are included as well