Intersection-Link Representations of Graphs

Abstract

We consider drawings of graphs that contain dense subgraphs. We introduce intersection-link representations for such graphs, in which each vertex $u$ is represented by a geometric object $R(u)$ and each edge $(u,v)$ is represented by the intersection between $R(u)$ and $R(v)$, if it belongs to a dense subgraph, or by a curve connecting the boundaries of $R(u)$ and $R(v)$, otherwise. We study a notion of planarity, called ${\rm C{\small LIQUE} P{\small LANARITY}}$, for intersection-link representations of graphs in which the dense subgraphs are cliques.