On a conjecture of Gentner and Rautenbach

António Girão; Gábor Mészáros; Stephen G. Z. Smith

On a conjecture of Gentner and Rautenbach

Combinatorics 2017-12-15 v3

Authors: António Girão , Gábor Mészáros , Stephen G. Z. Smith

Abstract

Gentner and Rautenbach conjectured that the size of a minimum zero forcing set in a connected graph on $n$ vertices with maximum degree $3$ is at most $\frac{1}{3}n+2$ . We disprove this conjecture by constructing a collection of connected graphs $\{G_n\}$ with maximum degree 3 of arbitrarily large order having zero forcing number at least $\frac{4}{9}|V(G_n)|$ .

Keywords

zero forcing set connected graph maximum degree 3 conjecture counterexample

Cite

@article{arxiv.1611.07513,
  title  = {On a conjecture of Gentner and Rautenbach},
  author = {António Girão and Gábor Mészáros and Stephen G. Z. Smith},
  journal= {arXiv preprint arXiv:1611.07513},
  year   = {2017}
}

Comments

Typos corrected, Title changed, Abstract changed. Paper is only oriented around the counterexample

On a conjecture of Gentner and Rautenbach

Abstract

Keywords

Cite

Comments

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