Three-dimensional symmetric tensor fields have a wide range of applications in solid and fluid mechanics. Recent advances in the topological analysis of 3D symmetric tensor fields focus on the local behaviors of tensor fields at degenerate points, which usually form curves. In this paper, we make a number of observations about tensor field topology that are more global in nature. For instance, ...

The two-coloring number of graphs, which was originally introduced in the study of the game chromatic number, also gives an upper bound on the degenerate chromatic number as introduced by Borodin. It is proved that the two-coloring number of any planar graph is at most nine. As a consequence, the degenerate list chromatic number of any planar graph is at most nine. It is also shown that the deg...

In this paper we classify static plane symmetric spacetimes according to their matter collineations. These have been studied for both cases when the energy-momentum tensor is non-degenerate and also when it is degenerate. It turns out that the non-degenerate case yields either four, five, six, seven or ten independent matter collineations in which four are isometries and the rest are proper. Th...