Monotone Drawings of Graphs with Fixed Embedding [chapter]

Patrizio Angelini, Walter Didimo, Stephen Kobourov, Tamara Mchedlidze, Vincenzo Roselli, Antonios Symvonis, Stephen Wismath
2012 Lecture Notes in Computer Science  
A drawing of a graph is a monotone drawing if for every pair of vertices u and v, there is a path drawn from u to v that is monotone in some direction. In this paper we investigate planar monotone drawings in the fixed embedding setting, i.e., a planar embedding of the graph is given as part of the input that must be preserved by the drawing algorithm. In this setting we prove that every planar graph on n vertices admits a planar monotone drawing with at most two bends per edge and with at most
more » ... 4n − 10 bends in total; such a drawing can be computed in linear time and in polynomial area. We also show that two bends per edge are sometimes necessary on a linear number of edges of the graph. Furthermore, we investigate subclasses of planar graphs that can be realized as embedding-preserving monotone drawings with straight-line edges, and we show that biconnected embedded planar graphs and outerplane graphs always admit such drawings, which can be computed in linear time. ⋆ Research supported in part by the MIUR project AlgoDEEP prot. 2008TFBWL4. Work on these results began at the 6th Bertinoro Workshop on Graph drawing. Discussion with other participants is gratefully acknowledged.
doi:10.1007/978-3-642-25878-7_36 fatcat:d6ofhrdr6bex5opoir45xg2nue