8,866 research outputs found

    Chromosome structure and DNA organisation

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    Construction of planar triangulations with minimum degree 5

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    AbstractIn this article, we describe a method of constructing all simple triangulations of the sphere with minimum degree 5; equivalently, 3-connected planar cubic graphs with girth 5. We also present the results of a computer program based on this algorithm, including counts of convex polytopes of minimum degree 5

    The Generation of Fullerenes

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    We describe an efficient new algorithm for the generation of fullerenes. Our implementation of this algorithm is more than 3.5 times faster than the previously fastest generator for fullerenes -- fullgen -- and the first program since fullgen to be useful for more than 100 vertices. We also note a programming error in fullgen that caused problems for 136 or more vertices. We tabulate the numbers of fullerenes and IPR fullerenes up to 400 vertices. We also check up to 316 vertices a conjecture of Barnette that cubic planar graphs with maximum face size 6 are hamiltonian and verify that the smallest counterexample to the spiral conjecture has 380 vertices.Comment: 21 pages; added a not
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