Computational geometry: an introduction
Computational geometry: an introduction
Graph Drawing: Algorithms for the Visualization of Graphs
Graph Drawing: Algorithms for the Visualization of Graphs
Drawing c-planar biconnected clustered graphs
Discrete Applied Mathematics
Convex drawings of graphs with non-convex boundary constraints
Discrete Applied Mathematics
Convex grid drawings of plane graphs with rectangular contours
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
An algorithm for constructing star-shaped drawings of plane graphs
Computational Geometry: Theory and Applications
Theoretical Computer Science
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In this paper, we present results on convex drawings of hierarchical graphs and clustered graphs. A convex drawing is a planar straight-line drawing of a plane graph, where every facial cycle is drawn as a convex polygon. Hierarchical graphs and clustered graphs are useful graph models with structured relational information. Hierarchical graphs are graphs with layering structures; clustered graphs are graphs with recursive clustering structures. We first present the necessary and sufficient conditions for a hierarchical plane graph to admit a convex drawing. More specifically, we show that the necessary and sufficient conditions for a biconnected plane graph due to Thomassen [C. Thomassen, Plane representations of graphs, in: J.A. Bondy, U.S.R. Murty (Eds.), Progress in Graph Theory, Academic Press, 1984, pp. 43-69] remains valid for the case of a hierarchical plane graph. We then prove that every internally triconnected clustered plane graph with a completely connected clustering structure admits a ''fully convex drawing,'' a planar straight-line drawing such that both clusters and facial cycles are drawn as convex polygons. We also present algorithms to construct such convex drawings of hierarchical graphs and clustered graphs.