Tag Archives: bound

Chromatic number of the plane roundup

Posted on June 28, 2018 by Brent

I’ve had fun writing about the Hadwiger-Nelson problem to determine the chromatic number of the plane, but I think this will be my last post on the topic for now! More 7-colorings Of course, the original point of the hexagonal … Continue reading →

Posted in geometry | Tagged , , , , , , , , | 7 Comments

The chromatic number of the plane, part 4: an upper bound

Posted on June 2, 2018 by Brent

In my previous posts I explained lower bounds for the Hadwiger-Nelson problem: we know that the chromatic number of the plane is at least 5 because there exist unit distance graphs which we know need at least 5 colors. Someday, … Continue reading →

Posted in geometry, proof | Tagged , , , , , , | Comments Off on The chromatic number of the plane, part 4: an upper bound

The chromatic number of the plane, part 3: a new lower bound

Posted on May 15, 2018 by Brent

In my previous post I explained how we know that the chromatic number of the plane is at least 4. If we can construct a unit distance graph (a graph whose edges all have length ) which needs at least … Continue reading →

Posted in geometry, proof | Tagged , , , , , | 1 Comment

The chromatic number of the plane, part 2: lower bounds

Posted on May 1, 2018 by Brent

In a previous post I explained the Hadwiger-Nelson problem—to determine the chromatic number of the plane—and I claimed that we now know the answer is either 5, 6, or 7. In the following few posts I want to explain how … Continue reading →

Posted in geometry, proof | Tagged , , , , , | 3 Comments