We consider a triangle lattice in the plane instead of an usual quadrangle lattice, and study some discrete structure problems on the triangle lattice. Namely, we consider life-games, graph drawings, Voronoi diagrams, channel routing problems, and other distributing problems on the triangle lattice in the plane, which are usually considered on the quadrangle lattice. The usual quadrangle lattice is not a maximal planar graph, but the triangle lattice is a maximal planar graph. Moreover edges of the usual lattice are parallel to x-axis or y-axis, and have only four directions. On the other hand, edges of the triangle lattice have six directions, and so its edges are distributed more uniformly than the usual lattice. From these point of view, we define some problems on the triangle lattice, and show that the triangle lattice has some advantage of these problems by some solutions obtained by computer. \n 平面上の3角格子において,ライフゲーム,平面グラフの描画,ボロノイ図,配線問題など考える.これらは従来普通の格子,すなわち4角格子において考えられ,また研究されてきた問題である.しかし,平面グラフとしてみたとき,3角格子は4角格子よりも密で均一性が高い.これからより良い解とか,4角格子とは異なる特色のある振る舞いが期待されるが,実際上の問題においてそのような結果を得た.これらの結果をまとめて報告する.
BKSJ250006.pdf (811.7 kB)
