منابع مشابه
Pointed Encompassing Trees
It is shown that for any set of disjoint line segments in the plane there exists a pointed binary encompassing tree, that is, a spanning tree on the segment endpoints that contains all input segments, has maximal degree three, and such that every vertex is incident to an angle greater than π. As a consequence, it follows that every set of disjoint line segments has a bounded degree pseudo-trian...
متن کاملPointed Binary Encompassing Trees
We show that for any set of disjoint line segments in the plane there exists a pointed binary encompassing tree T , that is, a spanning tree on the segment endpoints that contains all input segments, has maximum degree three, and every vertex v ∈ T is pointed, that is, v has an incident angle greater than π. Such a tree can be completed to a minimum pseudo-triangulation. In particular, it follo...
متن کاملCoxeter orbits and Brauer trees
We study the cohomology with modular coefficients of Deligne-Lusztig varieties associated to Coxeter elements. Under some torsion-free assumption on the cohomology we derive several results on the principal l-block of a finite reductive group G(Fq) when the order of q modulo l is assumed to be the Coxeter number. These results include the determination of the planar embedded Brauer tree of the ...
متن کاملTriangulations without pointed spanning trees
Problem 50 in the Open Problems Project of the computational geometry community asks whether any triangulation on a point set in the plane contains a pointed spanning tree as a subgraph. We provide a counterexample. As a consequence we show that there exist triangulations which require a linear number of edge flips to become Hamiltonian.
متن کاملPointed binary encompassing trees: Simple and optimal
For n disjoint line segments in the plane we construct in optimal O(n log n) time an encompassing tree of maximal degree three such that every vertex is pointed. Moreover, at every segment endpoint all incident edges lie in a halfplane defined by the incident input segment.
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2001
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.8928