4,988 research outputs found
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Graph Theory
This is the report on an Oberwolfach conference on graph theory, held 16-22 January 2005. There were three main components to the event: 5-minute presentations, lectures, and workshops. All participants were asked to give a 5-minute presentation of their interests on the first day, and subsequent days were divided into lectures and workshops. The latter ranged over many different topics, but the main three topics were: infinite graphs, topological methods and their use to prove theorems in graph theory, and Rota’s conjecture for matroids
Asymptotic enumeration and limit laws for graphs of fixed genus
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
where , and 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
This article deals with the construction of surfaces that are suitable for
representing pentachords or 5-pitch segments that are in the same 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
Retinal images and accomodation control mechanism under conditions of space flight stres
Planar graph coloring avoiding monochromatic subgraphs: trees and paths make things difficult
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
Recommended from our members
Graph Theory
This was a workshop on graph theory, with a comprehensive approach. Highlights included the emerging theories of sparse graph limits and of infinite matroids, new techniques for colouring graphs on surfaces, and extensions of graph minor theory to directed graphs and to immersion
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