Rosenfeld’s Odd-Distance Problem

Posted on February 21, 2009 by

 

Moshe Rosenfeld’s odd-distance problem: Let G be the graph whose vertices are points in the plane and two vertices form an edge if their distance is an odd integer. Is the chromatic number of this graph finite?

 

Here is a link to a paper on the problem by Hayri Ardal, Jan Manuch, Moshe Rosenfeld, Shaharon Shelah, and Ladislav Stacho.

About these ads
This entry was posted in Combinatorics, Open problems. Bookmark the permalink.

One Response to Rosenfeld’s Odd-Distance Problem

  1. Gil Kalai says:
    May 20, 2009 at 2:37 pm

    Update: Moshe is here, and he just told me that it follows from a theorem of Furstenberg, Katzenelson, and Weiss that if every color class is measurable than infinitely many colors are needed!

    Reply

Leave a Reply

Fill in your details below or click an icon to log in:

Gravatar
WordPress.com Logo

You are commenting using your WordPress.com account. ( Log Out / Change )

Twitter picture

You are commenting using your Twitter account. ( Log Out / Change )

Facebook photo

You are commenting using your Facebook account. ( Log Out / Change )

Cancel

Connecting to %s