  In this work we consider Byzantine Consensus on undirected communication
graphs under the local broadcast model. In the classical point-to-point
communication model the messages exchanged between two nodes $u, v$ on an edge
$uv$ of $G$ are private. This allows a faulty node to send conflicting
information to its different neighbours, a property called equivocation. In
contrast, in the local broadcast communication model considered here, a message
sent by node $u$ is received identically by all of its neighbours. This
restriction to broadcast messages provides non-equivocation even for faulty
nodes. In prior results [10, 11] it was shown that in the local broadcast model
the communication graph must be $(\lfloor 3f/2 \rfloor +1)$-connected and have
degree at least $2f$ to achieve Byzantine Consensus. In this work we show that
this network condition is tight.
