Further results on arc and bar k-visibility graphs

We consider visibility graphs involving bars and arcs in which lines of sight can pass through at most k objects. We prove a new edge bound for arc k-visibility graphs, provide maximal constructions for arc visibility graphs and semi-arc k-visibility graphs, and give a complete characterization of semi-arc visibility graphs. We further show that the family of arc i-visibility graphs is never contained in the family of bar j-visibility graphs for any i and j, and that the family of bar i-visibility graphs is not contained in the family of bar j-visibility graphs for i , j. Finally, we give the first thickness bounds for arc and semi-arc k-visibility graphs.