The kth upper chromatic number of the line

✍ Scribed by Aaron Abrams

• Book ID: 103061481
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 252 KB
• Volume: 169
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(95)00161-o

✦ Synopsis

Let S C ~', and let k E •. Greenwell and Johnson [3] define ~k)(S) to be the smallest integer m (if such an integer exists) such that for every k × m array D = (dq) of positive real numbers, S can be colored with the colors Ca ..... Cm such that no two points of S which are a (Euclidean) distance dij apart are both colored Cj, for all 1 <~i<~k and 1 <~j<~m. If no such integer exists then we say that ~k)(S) = exp. In this paper we show that ;~k)([~) is finite for all k.