%0 Conference Paper %1 fikkms-smdpg-socg16 %A Felsner, Stefan %A Igamberdiev, Alexander %A Kindermann, Philipp %A Klemz, Boris %A Mchedlidze, Tamara %A Scheucher, Manfred %B Proceedings of the 32nd International Symposium on Computational Geometry (SoCG'16) %D 2016 %E Fekete, Sándor %E Lubiw, Anna %I Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik %K drawing graph monotone myown planar %P 37:1--37:15 %R 10.4230/LIPIcs.SoCG.2016.37 %T Strongly Monotone Drawings of Planar Graphs %V 51 %X A straight-line drawing of a graph is a monotone drawing if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a strongly monotone drawing if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graphs, outerplanar graphs, and 2-trees. The drawings of 3-connected planar graphs are based on primal-dual circle packings. Our drawings of outerplanar graphs depend on a new algorithm that constructs strongly monotone drawings of trees which are also convex. For irreducible trees, these drawings are strictly convex.

@inproceedings{fikkms-smdpg-socg16, abstract = {A straight-line drawing of a graph is a \emph{monotone drawing} if for each pair of vertices there is a path which is monotonically increasing in some direction, and it is called a \emph{strongly monotone drawing} if the direction of monotonicity is given by the direction of the line segment connecting the two vertices. We present algorithms to compute crossing-free strongly monotone drawings for some classes of planar graphs; namely, 3-connected planar graphs, outerplanar graphs, and 2-trees. The drawings of 3-connected planar graphs are based on primal-dual circle packings. Our drawings of outerplanar graphs depend on a new algorithm that constructs strongly monotone drawings of trees which are also convex. For irreducible trees, these drawings are strictly convex.}, added-at = {2016-05-30T13:06:53.000+0200}, arxiv = {https://arxiv.org/abs/1601.01598}, author = {Felsner, Stefan and Igamberdiev, Alexander and Kindermann, Philipp and Klemz, Boris and Mchedlidze, Tamara and Scheucher, Manfred}, biburl = {https://www.bibsonomy.org/bibtex/285562b1a09aafef54527ed371fba76f6/kindermann}, booktitle = {Proceedings of the 32nd International Symposium on Computational Geometry (SoCG'16)}, doi = {10.4230/LIPIcs.SoCG.2016.37}, editor = {Fekete, S{\'a}ndor and Lubiw, Anna}, interhash = {ecc40ce04388c19c2d33f7c6d0dbbc92}, intrahash = {85562b1a09aafef54527ed371fba76f6}, keywords = {drawing graph monotone myown planar}, month = jun, pages = {37:1--37:15}, publisher = {Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik}, series = {LIPIcs}, slides = {http://www1.pub.informatik.uni-wuerzburg.de/pub/kindermann/slides/2016-eurocg-strongly_monotone-boris.pdf}, timestamp = {2018-09-18T07:13:12.000+0200}, title = {Strongly Monotone Drawings of Planar Graphs}, volume = 51, year = 2016 }