# Dr DAVE COULSON

Position:
Fellow (Associate)
Research Groups:
Recent Publications:
• A dense distance 1 excluding set in R^3. (2007) more
• On the chromatic number of plane tilings (2004) more
• A 15-colouring of 3-space omitting distance one (2002) more

Selected Publications

Extra Information:
We say that we have a chromatic colouring of n-space if we assign each point of n-space to a set and there is some distance d (an excluded distance) so that no two points in the same set are distance d apart. The minimum number of sets needed is known as the chromatic number of n-space.

At the moment it is known only that the chromatic number of two space lies between 4 and 7 (inclusive) and that the chromatic number of three space lies between 5 and 15 (inclusive).

A polychromatic colouring of n-space is similar to a chromatic colouring of n-space but we allow each set to have an excluded distance that is different from another set (rather than a common one d).

There are polychromatic colourings of 2-space with 6 sets bettering the most efficient known chromatic colouring with 7 sets. It is not known whether 3-space admits a polychromatic colouring with less than 15 sets (the number of sets in the most efficient chromatic colouring of 3-space uses 15 sets).