Volume 55 (2023)
Volume 54 (2022)
Volume 53 (2021)
Volume 52 (2020)
Volume 51 (2019)
Volume 50 (2018)
Volume 49 (2017)
Volume 48 (2016)
Volume 47 (2016)
Volume 46 (2015)
Volume 45 (2014)
Volume 44 (2013)
Volume 43 (2009)
Volume 42 (2008)
Volume 41 (2007)
A note on the approximability of the tenacity of graphs

Vahid Heidari; Dara Moazzami

Volume 52, Issue 2 , December 2020, , Pages 149-157

https://doi.org/10.22059/jac.2020.79270

Abstract
  In this paper we show that, if $NP\neq ZPP$, for any $\epsilon > 0$, the tenacity of graphwith $n$ vertices is not approximable in polynomial time within a factor of$\frac{1}{2} \left( \frac{n-1}{2} \right) ^{1-\epsilon}$.  Read More

Tenacious Graph is NP-hard

Dara Moazzami

Volume 51, Issue 2 , December 2019, , Pages 127-134

https://doi.org/10.22059/jac.2019.75276

Abstract
  The tenacity of a graph $G$, $T(G)$, is defined by$T(G) = min\{\frac{\mid S\mid +\tau(G-S)}{\omega(G-S)}\}$, where theminimum is taken over all vertex cutsets $S$ of $G$. We define$\tau(G - S)$ to be the number of the vertices in the largestcomponent of the graph $G-S$, and $\omega(G-S)$ be the number ...  Read More