On a conjecture of Gentner and Rautenbach
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 $\frac{4}{9}|V(G_n)|$.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2016
- DOI:
- 10.48550/arXiv.1611.07513
- arXiv:
- arXiv:1611.07513
- Bibcode:
- 2016arXiv161107513G
- Keywords:
-
- Mathematics - Combinatorics
- E-Print:
- Typos corrected, Title changed, Abstract changed. Paper is only oriented around the counterexample