On Grounded L-Graphs and their Relatives

  • Vít Jelínek
  • Martin Töpfer


We consider the graph classes Grounded-L and Grounded-{𝖫,⅃} corresponding to graphs that admit an intersection representation by 𝖫-shaped curves (or 𝖫-shaped and ⅃-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.

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