平面上の回路接続における最小交差問題

抄録

The problem of the least intersection of circuit connection on a plane is one concerned with the plan of circuit connection. The intersection number of connected wires is to be made smallest on a plane. Such a problem as this is a fundamental problem as the field in which to realize circuit connection is two dimensional space like a board of printed circuit. In this report, the problem is divided into two part: one deals with connection on a half plane on which circuit elements are ranged on the boundary line; the other is concerned with connection on a plane in general. And the infimum of intersection number is found as all circuit elements are connected to each other using a single wire. In case of mentioned connection on a half plane, it is shown to be an ideal plan of connection as compared with the infimum. While connection plans which are not ideal but practical are proposed in case of connecting on a plane. Foregoing connection plans are applied to a problem of printed circuit, and then a upper bound of hole number bored in a board of printed circuit is found for averting intersections of connected wires. This result is interpreted as a part of fundamental theory of printed circuit on general surface.