4,988 research outputs found

    Asymptotic enumeration and limit laws for graphs of fixed genus

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    It is shown that the number of labelled graphs with n vertices that can be embedded in the orientable surface S_g of genus g grows asymptotically like c(g)n5(g−1)/2−1γnn!c^{(g)}n^{5(g-1)/2-1}\gamma^n n! where c(g)>0c^{(g)}>0, and γ≈27.23\gamma \approx 27.23 is the exponential growth rate of planar graphs. This generalizes the result for the planar case g=0, obtained by Gimenez and Noy. An analogous result for non-orientable surfaces is obtained. In addition, it is proved that several parameters of interest behave asymptotically as in the planar case. It follows, in particular, that a random graph embeddable in S_g has a unique 2-connected component of linear size with high probability

    A Tonnetz Model for pentachords

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    This article deals with the construction of surfaces that are suitable for representing pentachords or 5-pitch segments that are in the same T/IT/I class. It is a generalization of the well known \"Ottingen-Riemann torus for triads of neo-Riemannian theories. Two pentachords are near if they differ by a particular set of contextual inversions and the whole contextual group of inversions produces a Tiling (Tessellation) by pentagons on the surfaces. A description of the surfaces as coverings of a particular Tiling is given in the twelve-tone enharmonic scale case.Comment: 27 pages, 12 figure

    Vision during manned booster operation Final report

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    Retinal images and accomodation control mechanism under conditions of space flight stres

    Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult

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    We consider the problem of coloring a planar graph with the minimum number of colors such that each color class avoids one or more forbidden graphs as subgraphs. We perform a detailed study of the computational complexity of this problem
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