... hosts.¹

More precisely, Core$(h)$ is a core constrained to contain $h$. That is, $\mbox{\emph{Core}$(h)$} \setminus \{ h\}$ may itself be minimal, but we require $h \in$ Core$(h)$.

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... of 5.²

To meet this bound, number the hosts in $\cal H$ from 0 to $\vert{\cal H}\vert - 1$. Let Core$(h)$ be the hosts $\{h, h \oplus 1, h \oplus 2, h \oplus 3, h \oplus 4\}$ where $\oplus$ is addition modulo $\vert\cal H\vert$.

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