Trees are almost prime

被引：14
|
作者：
Pikhurko, Oleg [1 ]
机构：
[1] Carnegie Mellon Univ, Dept Math Sci, Pittsburgh, PA 15213 USA
来源：
DISCRETE MATHEMATICS | 2007年 / 307卷 / 11-12期
关键词：
Entringer's conjecture; prime graphs; trees;
D O I：
10.1016/j.disc.2005.11.083
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let S-n denote the graph on {1,..., n) in which two numbers are adjacent if and only if they are coprime. Around 1980 Entringer conjectured that Sn contains every tree of order n as a subgraph. Here we show that this conjecture is true for all n <= 50. Further positive evidence is provided by our main result that S, contains every tree of order (1 - o(1))n. (c) 2006 Published by Elsevier B.V.
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页码：1455 / 1462
页数：8
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