| 素距离图的着色与距离集的分类 |
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| 引用本文： | 刘儒英.素距离图的着色与距离集的分类[J].青海师范大学学报(自然科学版),1993(2). |
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| 作者姓名： | 刘儒英 |
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| 作者单位： | 青海师范大学数学系 |
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| 摘 要： | 设 P 表示全体素数的集合,D(?)P,令 Z(D)表示这样一个图:它的顶点集是全体整数的集合,两个顶点 x 和 y 之间有边连结当且仅当(?)x—y(?)D.文1]证明了.对任意 D(?)P,Z(D)的色数至多是4,因而可按照 Z(D)的色数把 P 的所有子集 D 分为四类,本文给出了两组新的4类子集簇,并给出若干个 D 是3类子集的充分条件。
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| 关 键 词： | 图 素距离图 着色 |
COLOURING PRIME DISTANCE GRAPH AND CLASSIFICATION OF DISTANCE SET |
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| Liu Ruying.COLOURING PRIME DISTANCE GRAPH AND CLASSIFICATION OF DISTANCE SET[J].Journal of Qinghai Normal University(Natural Science Edition),1993(2). |
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| Authors: | Liu Ruying |
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| Institution: | Qinghai Normal University |
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| Abstract: | Let P denote the ser of all prime numbers,and D(?)P.Let Z(D) denote the graph with the integers as its vertex and the edges between those pairs of integers with absolute differ- ence in the set D.In it is shown that for any D(?)P,the chromatic numder of Z(D) is at most 4,therefore we can allocate the D to four classes,according as chromatic number of Z (D).In this paper,two new families of class 4 sets are given.Some sufficient conditions for D to be class 3 set are also given. |
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| Keywords: | Graph Frime distance graph Colouring |
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