TY - EJOUR
DO - 10.1016/j.comgeo.2014.01.003
AB - We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions. We prove that Delta - 1 edge slopes suffice for every outerplanar graph with maximum degree Delta >= 4. This improves on the previous bound of O(Delta(5)), which was shown for planar partial 3-trees, a superclass of outerplanar graphs. The bound is tight: for every Delta >= 4 there is an outerplanar graph with maximum degree Delta that requires at least Delta - 1 distinct edge slopes in an outerplanar straight-line drawing. (C) 2014 Elsevier B.V. All rights reserved.
T1 - Outerplanar graph drawings with few slopes
IS - 5
DA - 2014
AU - Knauer, Kolja
AU - Micek, Piotr
AU - Walczak, Bartosz
JF - Computational Geometry-Theory And Applications
SP - 614-624
VL - 47
EP - 614-624
PB - Elsevier Science Bv
PP - Amsterdam
ID - 198560
KW - Outerplanar graph
KW - Striagh-line drawing
KW - Slope number
SN - 0925-7721
ER -