Bounding the size of square-free subgraphs of the hypercube

被引：19
|
作者：
Thomason, Andrew [1 ]
Wagner, Peter [1 ]
机构：
[1] DPMMS, Ctr Math Sci, Cambridge CB3 0WB, England
来源：
DISCRETE MATHEMATICS | 2009年 / 309卷 / 06期
关键词：
Hypercube; n-cube; 4-cycle; CUBE;
D O I：
10.1016/j.disc.2008.02.015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We investigate the maximum size of a Subset of the edges of the n-cube that does not contain a square, or 4-cycle. The size of Such a subset is trivially at most 3/4 of the total number of edges, but the proportion was conjectured by Erdos to be asymptotically 1/2. Following a Computer investigation of the 4-cube and the 5-cube, we improve the known upper bound from 0.62284 ... to 0.62256 ... in the limit. (C) 2008 Elsevier B.V. All rights reserved.
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页码：1730 / 1735
页数：6
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