Software


01/Nov/2016: Around this date, I started experimenting a new method based on Kempe’s chains. Read the blogs I published starting from this: https://4coloring.wordpress.com/2016/02/23/four-color-theorem-back-to-the-basics/

I have implemented a Python algorithm that goes really fast coloring the edges of a planar graph.

See this video and then try it youself!

Note about the Python program: To try the Python program you need to have Sage. Follow Sage instructions to install it on your computer: http://www.sagemath.org.


This section is dedicated to the Java program I use to analyse maps.

Snapshots of the java application:

Downloads:

To download the software and the source code of the project go to the sourceforge site:

http://sourceforge.net/projects/maps-coloring/

Youtube channel (see it in action):

http://www.youtube.com/user/mariostefanutti

Documentation:

For now (08/Feb/2011) the software is undocumented. Best way to learn it it to start pushing buttons randomly. 😉 Don’t esitate to contact me if you need help.

JVM settings for 1.6 (to go a great deal faster than default settings):

  • java -Xms1500m -Xmx1500m -XX:+UseParallelGC -jar .jar

The information that follow are not valid for the last version of the software, because I implemented some code to optimize the generation of maps, as removing isomorphic maps. For example, with this flag enabled the generation of simplified maps with maxMethod = F and maxNumber = 12, returns just one map.

Just to start coloring some good maps follow these instructions:

  • Run the application using java -jar .jar (java 1.5> is needed)
  • Switch to maxMethod = F and set maxNumber = 10
  • Push start and wait the elaboration to finish
  • Filter out all maps that have faces with less than 4 edges (“-4” button)
  • At this point you should have 14 maps left
  • Browse and color them
  • To generate more complex maps you can copy the maps back into the todoList (“.|.” button)
  • Set maxMethod = MAPS and maxNumber = 10000
  • Push play, wait the end of the elaboration and filter
  • filter, play and copy back into the todo list … filter, play and copy …
  • After some iterations you can even risk to filter maps with less than 5 edges

Another method is:

    • Run the application using java -jar .jar (java 1.5> is needed)
    • Switch to maxMethod = F and set maxNumber = 12
    • Push start and wait the elaboration to finish (less than a minute if the java GC has been set properly)
    • Filter out all maps that have faces with less than 5 edges (“-5” button)
    • At this point you should have 10980 maps left (see here)
    • Browse and color them

Stucture of the project:

  • ct-core (core library for generating simplified maps)
  • ct-ui-swixml (standalone UI based on swixml an G – execute using java -jar)

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