Tree-width and its linear variant path-width play a central role for the graph minor relation. In particular, Robertson Seymour (1983) proved that every tree~$T$, class of graphs do not contain $T$ as has bounded path-width. For pivot-minor relation, rank-width take over from tree-width As such, it is natural to examine if rank-width. We first prove this statement false whenever tree caterpilla...

Graphs with circular symmetry, called webs, are relevant w.r.t. describing the stable set polytopes of two larger graph classes, quasi-line graphs [7,11] and claw-free graphs [6,7]. Providing a decent linear description of the stable set polytopes of claw-free graphs is a long-standing problem [8]. However, even the problem of finding all facets of stable set polytopes of webs is open. So far, ...

We study Rainich-like conditions for symmetric and trace-free tensors T. For arbitrary even rank we find a necessary and sufficient differential condition for a tensor to satisfy the source free field equation. For rank 4, in a generic case, we combine these conditions with previously obtained algebraic conditions to obtain a complete set of algebraic and differential conditions on T for it to ...