A lower bound on the stretch factor of Yao graph Y4

One of the most popular graphs in computational geometry is Yao graph, denotedconstructedby Yink.theForfolloeverywing.pointAroundset Seacin hthepointplanep andS, antheinplanetegerisk divided2, Yaointographk Yregulark is 2 cones with the apex at p. The set of all these cones is denoted by Cp. Then, for each cone C 2 Cp, an edge (p; r) is added to Yk, where r is the closest point in C to p. This study provides a lower bound of 3.8285 for the stretch factor of Y4 which can partially solve an open problem posed by Barba et al. (L. Barba et al., \New and Improved Spanning Ratios for Yao Graphs , Journal of Computational Geometry, 6(2), pp. 19{53 2015).