%0 Conference Paper %1 10.1007/978-3-319-73915-1_3 %A Angelini, Patrizio %A Chaplick, Steven %A De Luca, Felice %A Fiala, Jirí %A Hancl, Jaroslav %A Heinsohn, Niklas %A Kaufmann, Michael %A Kobourov, Stephen %A Kratochvíl, Jan %A Valtr, Pavel %B Proc. 25th Int. Symp. Graph Drawing & Network Vis. (GD'17) %C Cham %D 2017 %E Frati, Fabrizio %E Ma, Kwan-Liu %I Springer International Publishing %K conference myown publication %P 24--37 %R 10.1007/978-3-319-73915-1_3 %T On Vertex- and Empty-Ply Proximity Drawings %V 10692 %X We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-ply of a drawing is determined by the vertex covered by the maximum number of disks. The main motivation for considering this relaxation is to relate the concept of ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-ply number 1 can be seen as a weak proximity drawing, which we call empty-ply drawing. We show non-trivial relationships between the ply number and the vertex-ply number. Then, we focus on empty-ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the ply and the vertex-ply of planar drawings. %@ 978-3-319-73915-1

@inproceedings{10.1007/978-3-319-73915-1_3, abstract = {We initiate the study of the vertex-ply of straight-line drawings, as a relaxation of the recently introduced ply number. Consider the disks centered at each vertex with radius equal to half the length of the longest edge incident to the vertex. The vertex-ply of a drawing is determined by the vertex covered by the maximum number of disks. The main motivation for considering this relaxation is to relate the concept of ply to proximity drawings. In fact, if we interpret the set of disks as proximity regions, a drawing with vertex-ply number 1 can be seen as a weak proximity drawing, which we call empty-ply drawing. We show non-trivial relationships between the ply number and the vertex-ply number. Then, we focus on empty-ply drawings, proving some properties and studying what classes of graphs admit such drawings. Finally, we prove a lower bound on the ply and the vertex-ply of planar drawings.}, added-at = {2018-01-26T14:47:52.000+0100}, address = {Cham}, author = {Angelini, Patrizio and Chaplick, Steven and De Luca, Felice and Fiala, Ji{\v{r}}{\'i} and Han{\v{c}}l, Jaroslav and Heinsohn, Niklas and Kaufmann, Michael and Kobourov, Stephen and Kratochv{\'i}l, Jan and Valtr, Pavel}, biburl = {https://www.bibsonomy.org/bibtex/2c53dc50eabc2e66c588d1a9c9260861e/chaplick}, booktitle = {Proc. 25th Int. Symp. Graph Drawing & Network Vis. (GD'17)}, description = {On Vertex- and Empty-Ply Proximity Drawings | SpringerLink}, doi = {10.1007/978-3-319-73915-1_3}, editor = {Frati, Fabrizio and Ma, Kwan-Liu}, interhash = {901c2191a28b68cf2dcc4c3ff47a759f}, intrahash = {c53dc50eabc2e66c588d1a9c9260861e}, isbn = {978-3-319-73915-1}, keywords = {conference myown publication}, pages = {24--37}, publisher = {Springer International Publishing}, series = {LNCS}, timestamp = {2018-01-26T14:51:46.000+0100}, title = {On Vertex- and Empty-Ply Proximity Drawings}, volume = 10692, year = 2017 }