The paper disproves the natural generalization of Vizing's conjecture for (t,r) broadcast domination when r≥2, and provides density bounds and a faster search algorithm for grid patterns.
New upper bounds on the dista nce domination numbers of grids
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Bounds On $(t,r)$ Broadcast Domination of $n$-Dimensional Grids
The paper disproves the natural generalization of Vizing's conjecture for (t,r) broadcast domination when r≥2, and provides density bounds and a faster search algorithm for grid patterns.