Abstract
We consider the graph classes GROUNDED-L and GROUNDED-{L, inverted-L} corresponding to graphs that admit an intersection representation by L-shaped curves (or L-shaped and (inverted-L)-shaped curves, respectively), where additionally the topmost points of each curve are assumed to belong to a common horizontal line. We prove that GROUNDED-L graphs admit an equivalent characterisation in terms of vertex ordering with forbidden patterns.
We also compare these classes to related intersection classes, such as the grounded segment graphs, the monotone L-graphs (a.k.a. max point-tolerance graphs), or the outer-1-string graphs. We give constructions showing that these classes are all distinct and satisfy only trivial or previously known inclusions.