COLORING PRIME DISTANCE GRAPHS

被引：45

作者：

EGGLETON, RB

ERDOS, P

SKILTON, DK

机构：

[1] UNIV BRUNEI DARUSSALAM,DEPT MATH,GADONG 3186,BRUNEI

[2] HUNGARIAN ACAD SCI,BUDAPEST,HUNGARY

[3] IBM AUSTRALIA,ULTIMO,NSW 2007,AUSTRALIA

来源：

GRAPHS AND COMBINATORICS | 1990年 / 6卷 / 01期

关键词：

D O I：

10.1007/BF01787476

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Four colours are necessary and sufficient to colour all the integers so that any two with difference equal to a prime have different colours. We investigate the corresponding problem when the set D of prescribed differences is a proper subset of the primes. In particular, we prove that if D contains {2, 3} and also contains a pair of twin primes (one of which may be 3), then four colours are necessary. Numerous results regarding periodic colourings are also obtained. However, the problem of characterizing those sets D which necessitate four colours remains open. © 1990 Springer-Verlag.

引用

页码：17 / 32

页数：16