By Topic

Extremely Complex 4-Colored Rectangle-Free Grids: Solution of Open Multiple-Valued Problems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Bernd Steinbach ; Inst. of Comput. Sci., Freiberg Univ. of Min. & Technol., Freiberg, Germany ; Christian Posthoff

This paper aims at the rectangle-free coloring of grids using four colors. It has been proven in a well developed theory that there is an upper bound of rectangle-free 4-colorable grids as well as a lower bound of grids for which no rectangle-free color pattern of four colors exist. Between these tight bounds the grids of the size 17×17, 17×18, 18 × 17, and 18 ×18 are located for which it is not known until now whether a rectangle-free coloring by four colors exists. We present in this paper an approach that solves all these open problems. From another point of view this paper aims at the solution of a multiple-valued problem having an extremely high complexity. There are 1.16798 * 10195 different grids of four colors. It must be detected whether at least one of this hardly imaginable large number of patterns satisfies strong additional conditions. In order to solve this highly complex problem, several approaches were taken into account to find out properties of the problem which finally allowed us to calculate the solution.

Published in:

2012 IEEE 42nd International Symposium on Multiple-Valued Logic

Date of Conference:

14-16 May 2012