TY - JOUR
T1 - Maximizing maximal angles for plane straight-line graphs
AU - Aichholzer, O.
AU - Hackl, T.
AU - Hoffmann, M.
AU - Huemer, C.
AU - Santos, F.
AU - Speckmann, B.
AU - Vogtenhuber, B.
PY - 2013
Y1 - 2013
N2 - Let G=(S,E) be a plane straight-line graph on a finite point set S¿R2 in general position. The incident angles of a point p¿S in G are the angles between any two edges of G that appear consecutively in the circular order of the edges incident to p. A plane straight-line graph is called f-open if each vertex has an incident angle of size at least f. In this paper we study the following type of question: What is the maximum angle f such that for any finite set S¿R2 of points in general position we can find a graph from a certain class of graphs on S that is f-open? In particular, we consider the classes of triangulations, spanning trees, and spanning paths on S and give tight bounds in most cases.
AB - Let G=(S,E) be a plane straight-line graph on a finite point set S¿R2 in general position. The incident angles of a point p¿S in G are the angles between any two edges of G that appear consecutively in the circular order of the edges incident to p. A plane straight-line graph is called f-open if each vertex has an incident angle of size at least f. In this paper we study the following type of question: What is the maximum angle f such that for any finite set S¿R2 of points in general position we can find a graph from a certain class of graphs on S that is f-open? In particular, we consider the classes of triangulations, spanning trees, and spanning paths on S and give tight bounds in most cases.
U2 - 10.1016/j.comgeo.2012.03.002
DO - 10.1016/j.comgeo.2012.03.002
M3 - Article
SN - 0925-7721
VL - 46
SP - 17
EP - 28
JO - Computational Geometry
JF - Computational Geometry
IS - 1
ER -