4 papers
A new upper bound for angular resolution
Hiroyuki Miyata
The angular resolution of a planar straight-line drawing of a graph is the smallest angle formed by two edges incident to the same vertex. Garg and Tamassia (ESA '94) constructed a…
Complete combinatorial characterization of greedy-drawable trees
Hiroyuki Miyata, Reiya Nosaka
A (Euclidean) greedy drawing of a graph is a drawing in which, for any two vertices (), there is a neighbor vertex of that is closer to than to in the E…
A two-dimensional topological representation theorem for matroid polytopes of rank 4
Hiroyuki Miyata
The Folkman-Lawrence topological representation theorem, which states that every (loop-free) oriented matroid of rank can be represented as a pseudosphere arrangement on the $(…
On Combinatorial Properties of Points and Polynomial Curves
Hiroyuki Miyata
Many combinatorial properties of a point set in the plane are determined by the set of possible partitions of the point set by a line. Their essential combinatorial properties are…