Bounding the number of tolerable faults in majority-based systems
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
Stable sets of threshold-based cascades on the erdős-rényi random graphs
IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
On the non-progressive spread of influence through social networks
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Triggering cascades on undirected connected graphs
Information Processing Letters
Bounding the sizes of dynamic monopolies and convergent sets for threshold-based cascades
Theoretical Computer Science
| Hi-index | 0.00 |
The decycling number $\nabla(G)$ of a graph $G$ is the smallest number of vertices which can be removed from $G$ so that the resultant graph contains no cycles. In this paper, we study the decycling number for the family of graphs consisting of the Cartesian product of two cycles. We completely solve the problem of determining the decycling number of $C_m \square C_n$ for all $m$ and $n$. Moreover, we find a vertex set $T$ that yields a maximum induced tree in $C_m\square C_n$.