Homothetic Triangle Contact Representations of Planar Graphs

In this paper we study the problem of computing homothetic triangle contact representations of planar graphs. Since not all planar graphs admit such a representation, we concentrate on meaningful subfamilies of planar graphs and prove that: (i) every two-terminal seriesparallel digraph has a homothetic triangle contact representation, which can be computed in linear time; (ii) every partial planar 3-tree admits a homothetic triangle contact representation.