A Generalization of the Methods of Brass, Harboth, and Nieborg

Brendon Stanton

A Generalization of the Methods of Brass, Harboth, and Nieborg

Combinatorics 2014-05-26 v1

Authors: Brendon Stanton

Abstract

In 1995, Brass, Harborth and Nienborg disproved a conjecture of Erd\H{o}s when they showed that a $C_4$ -free subgraph of the hypercube, $Q_n$ , can have at least $(\frac 12 +\omega(1))e(Q_n)$ edges. In this paper, we generalize the idea of Brass, Harborth and Nienborg to provide good constructions of $Q_3$ -free subgraphs of $Q_n$ for some small values of $n$ .

Keywords

hypercube extremal graph theory forbidden subgraphs Brass-Harborth-Nienborg method Erd\H{o}s conjecture combinatorial constructions

Cite

@article{arxiv.1405.5957,
  title  = {A Generalization of the Methods of Brass, Harboth, and Nieborg},
  author = {Brendon Stanton},
  journal= {arXiv preprint arXiv:1405.5957},
  year   = {2014}
}

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