Which point sets admit a k-angulation?

For k >= 3, a k-angulation is a 2-connected plane graph in which every internal face is a k-gon. We say that a point set P admits a plane graph G if there is a straight-line drawing of G that maps V(G) onto P and has the same facial cycles and outer face as G. We investigate the conditions under which a point set P admits a k-angulation and find that, for sets containing at least 2k^2 points, the only obstructions are those that follow from Euler's formula.Comment: 13 pages, 7 figure

Optical conductivity in A3C60 (A=K, Rb)

We study the optical conductivity in A3C60 (A =K, Rb). The effects of the electron-phonon interaction is included to lowest order in the coupling strength lambda. It is shown that this leads to a narrowing of the Drude peak by a factor 1+lambda and a transfer of weight to a mid-infrared peak at somewhat larger energies than the phonon energy. Although this goes in the right direction, it is not sufficient to describe experiment.Comment: 5 pages, revtex, 2 figures more information at http://librix.mpi-stuttgart.mpg.de/docs/ANDERSEN/fullerene