Improved bounds on the stretch factor of Y4

We establish an upper bound of 13+82≲4.931 on the stretch factor of the Yao graph Y4∞ defined in the L∞-metric, improving upon the best previously known upper bound of 6.31. We also establish an upper bound of (11+72)4+22≲54.62 on the stretch factor of the Yao graph Y4 defined in the L2-metric, improving upon the best previously known upper bound of 663.