  Quantum information processing architectures typically only allow for
nearest-neighbour entanglement creation. In many cases, this prevents the
direct generation of GHZ states, which are commonly used for many communication
and computation tasks. Here, we show how to obtain GHZ states between nodes in
a network that are connected in a straight line, naturally allowing them to
initially share linear cluster states. We prove a strict upper bound of
$\lfloor (n+3)/2 \rfloor$ on the size of the set of nodes sharing a GHZ state
that can be obtained from a linear cluster state of $n$ qubits, using local
Clifford unitaries, local Pauli measurements, and classical communication.
Furthermore, we completely characterize all selections of nodes below this
threshold that can share a GHZ state obtained within this setting. Finally, we
demonstrate these transformations on the IBMQ Montreal quantum device for
linear cluster states of up to $n=19$ qubits.
