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We show that the Yao graph Y 4 in the L 2 metric is a spanner with stretch factor 8 √ 2(29+ 23 √ 2). Enroute to this, we also show that the Yao graph Y ∞ 4 in the L∞ metric is a plane spanner with stretch factor 8.
We show that, for any integer k ≥ 6, the Sparse-Yao graph Y Y 6k (also known as Yao-Yao) is a spanner with stretch factor 11.67. The stretch factor drops down to 4.75 for k ≥ 8.
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