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

Byzantine Consensus under Local Broadcast Model: Tight Sufficient Condition