| Summary: | In 2001, Erwin introduced broadcast domination in graphs. It is a variant of
classical domination where selected vertices may have different domination
powers. The minimum cost of a dominating broadcast in a graph $G$ is denoted
$\gamma_b(G)$. The dual of this problem is called multipacking: a multipacking
is a set $M$ of vertices such that for any vertex $v$ and any positive integer
$r$, the ball of radius $r$ around $v$ contains at most $r$ vertices of $M$ .
The maximum size of a multipacking in a graph $G$ is denoted mp(G). Naturally
mp(G) $\leq \gamma_b(G)$. Earlier results by Farber and by Lubiw show that
broadcast and multipacking numbers are equal for strongly chordal graphs. In
this paper, we show that all large grids (height at least 4 and width at least
7), which are far from being chordal, have their broadcast and multipacking
numbers equal.
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