Topological Inductive Constructions for Tight Surface Graphs

We investigate properties of sparse and tight surface graphs. In particular we derive topological inductive constructions for $$(2,2)$$ -tight surface graphs in the case of the sphere, the plane, the twice punctured sphere and the torus. In the case of the torus we identify all 116 irreducible base graphs and provide a geometric application involving contact graphs of configurations of circular arcs.