Chan C.-HHSU-CHUN YEN2021-09-022021-09-02201903029743https://www.scopus.com/inward/record.uri?eid=2-s2.0-85078523638&doi=10.1007%2f978-3-030-36412-0_7&partnerID=40&md5=937236fb7ec13890503374ed8dc6ba88https://scholars.lib.ntu.edu.tw/handle/123456789/580863In applications such as VLSI floorplanning and cartogram design, vertices of a graph are represented by geometric objects and edges are captured by contacts between those objects, which are examples of a drawing style called contact graph representations. We study the feasibility of using line segments, triangles and tetrahedra to realize point-side contact representations for a number of graph classes including oriented versions of outerplanar graphs, 2-trees and 3-trees. Our main results show that every orientation of a maximal outerplanar graph of out-degree at most two, a 2-tree of out-degree at most two, and a planar 3-tree of out-degree at most four enjoy point-side contact representations using line segments, triangles, and tetrahedra, respectively. Unlike undirected graphs for which a fairly large amount of results can be found in the literature in the study of contact representations, directed graphs remain largely unexplored, and our study advances this line of research a step further. ? 2019, Springer Nature Switzerland AG.Combinatorial optimization; Geometry; Graphic methods; Contact graphs; Drawing styles; Geometric objects; Large amounts; Outerplanar graph; Planar graph; Undirected graph; VLSI floorplanning; Directed graphs[SDGs]SDG11conference paper10.1007/978-3-030-36412-0_72-s2.0-85078523638