Aaron Slobodin, Gary MacGillivray, Wendy Myrvold
Published 2021-10-17, updated 2022-09-21Version 2
We establish upper and lower bounds for the 2-limited broadcast domination number of various grid graphs, in particular the Cartesian product of two paths, a path and a cycle, and two cycles. The upper bounds are derived by explicit constructions. The lower bounds are obtained via linear programming duality by finding lower bounds for the fractional 2-limited multipacking numbers of these graphs.
On $(t,r)$ broadcast domination of certain grid graphs
Proving exact values for the 2-limited broadcast domination number on grid graphs
On Linkedness of Cartesian Product of Graphs
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