Skip to main content

Advertisement

Log in

A Cellular Triangle Containing a Specified Point

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract.

 Let P be a set of finite points in the plane in general position, and let x be a point which is not contained in any of the lines passing through at least two points of P. A line l is said to be a k-bisector if both of the two closed half-planes determined by l contain at least k points of P. We show that if any line passing through x is a -bisector and does not contain two or more points of P, then there exist three points P 1, P 2, P 3 of P such that ΔP 1 P 2 P 3 contains x and does not contain points of P in its interior, and such that each of the lines passing through two of them is a -bisector.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Author information

Authors and Affiliations

Authors

Additional information

Received: October 16, 1995 / Revised: October 16, 1996

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tokunaga, Si. A Cellular Triangle Containing a Specified Point. Graphs Comb 15, 239–247 (1999). https://doi.org/10.1007/s003730050057

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s003730050057

Navigation