An 18-colouring of 3-space omitting distance one

✍ Scribed by D. Coulson

• Book ID: 104113809
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 263 KB
• Volume: 170
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/s0012-365x(96)00309-3

✦ Synopsis

It is known that the number of colours X(R 3) necessary to colour each point of 3-space so that no two points lying distance 1 apart have the same colour lies between 5 and 21. The upper bound of 21 was established by constructing a colouring with the 1-excluded property. In this paper a l-excluded, 18-colouring is constructed.