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.
引用
收藏
页码：1455 / 1462
页数：8
相关论文
共 50 条
  • [21] ON REPRESENTATION OF LARGE EVEN INTEGERS AS SUMS OF PRIME + ALMOST PRIME
    UCHIYAMA, M
    UCHIYAMA, S
    PROCEEDINGS OF THE JAPAN ACADEMY, 1964, 40 (03): : 150 - &
  • [22] Prime and almost prime integral points on principal homogeneous spaces
    Nevo, Amos
    Sarnak, Peter
    ACTA MATHEMATICA, 2010, 205 (02) : 361 - 402
  • [23] Almost-prime values of reducible polynomials at prime arguments
    Franze, C. S.
    Kao, P. H.
    JOURNAL OF NUMBER THEORY, 2020, 210 : 292 - 312
  • [24] n-almost prime submodules
    S. Moradi
    A. Azizi
    Indian Journal of Pure and Applied Mathematics, 2013, 44 : 605 - 619
  • [25] Commentary: Almost ready for prime time
    Wei, Lawrence M.
    JTCVS TECHNIQUES, 2020, 3 : 174 - 175
  • [26] SUMS OF ALMOST EQUAL PRIME SQUARES
    Li, Hongze
    Wu, Jie
    FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 2008, 38 (01) : 49 - 65
  • [27] On Decidable Categoricity and Almost Prime Models
    Goncharov S.S.
    Harizanov V.
    Miller R.
    Siberian Advances in Mathematics, 2020, 30 (3) : 200 - 212
  • [28] Additive problems with almost prime squares
    Valentin Blomer
    Lasse Grimmelt
    Junxian Li
    Simon L. Rydin Myerson
    Geometric and Functional Analysis, 2023, 33 : 1173 - 1242
  • [29] Sums of almost equal prime cubes
    F. Zhao
    Acta Mathematica Hungarica, 2010, 126 : 279 - 293
  • [30] Additive problems with almost prime squares
    Blomer, Valentin
    Grimmelt, Lasse
    Li, Junxian
    Myerson, Simon L. Rydin L.
    GEOMETRIC AND FUNCTIONAL ANALYSIS, 2023, 33 (05) : 1173 - 1242
12345