  Motivated by the observation of ferromagnetism in carbon foams, a massive
search for (meta)stable disorder structures of elemental carbon is performed by
a generate and test approach. We use the Density Functional based program
SIESTA to optimize the structures and calculate the electronic spectra and spin
densities. About 1% of the 24000 optimized structures presents magnetic
moments, a necessary but not sufficient condition for intrinsic magnetic order.
We analyze the results using elements of graph theory. Although the relation
between structure and the occurrence of magnetic moments is not yet fully
clarified, we give some minimal requirements for this possibility, such as the
existence of three-fold coordinated atoms surrounded by four-fold coordinated
atoms. We discuss in detail the most promising structures.
