Parity of network size can be locally certified with constant bits using IDs at radius 2 or in bounded-expansion graphs at radius 1, but needs Ω(log log* n) bits in anonymous radius-1 model.
9 Laurent Feuilloley, Nicolas Bousquet, and Théo Pierron
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The local complexity of certifying parity
Parity of network size can be locally certified with constant bits using IDs at radius 2 or in bounded-expansion graphs at radius 1, but needs Ω(log log* n) bits in anonymous radius-1 model.