Drawing Cubic Graphs with the Four Basic Slopes
نویسندگان
چکیده
We show that every cubic graph can be drawn in the plane with straight-line edges using only the four basic slopes {0, π/4, π/2, 3π/4}. We also prove that four slopes have this property if and only if we can draw K4 with them.
منابع مشابه
Drawing Cubic Graphs with at Most Five Slopes
We show that every graph G with maximum degree three has a straight-line drawing in the plane using edges of at most five different slopes. Moreover, if G is connected and has at least one vertex of degree less than three, then four directions suffice.
متن کاملReally Straight Graph Drawings
We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes, and that every cubic 3-connected plane graph has a plane drawing with ...
متن کاملar X iv : c s . D M / 0 40 51 12 v 1 3 1 M ay 2 00 4 Really Straight Graph Drawings ∗
We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing ...
متن کاملar X iv : c s / 04 05 11 2 v 1 [ cs . D M ] 3 1 M ay 2 00 4 Really Straight Graph Drawings ∗
We study straight-line drawings of graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5n/2 segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane drawing ...
متن کاملm at h . C O ] 1 9 Ju n 20 06 Drawings of Planar Graphs with Few Slopes and Segments ∗
We study straight-line drawings of planar graphs with few segments and few slopes. Optimal results are obtained for all trees. Tight bounds are obtained for outerplanar graphs, 2-trees, and planar 3-trees. We prove that every 3-connected plane graph on n vertices has a plane drawing with at most 5 2 n segments and at most 2n slopes. We prove that every cubic 3-connected plane graph has a plane ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011