Odd Yao-Yao Graphs are Not Spanners
نویسندگان
چکیده
It is a long standing open problem whether Yao-Yao graphs YYk are all spanners [26]. Bauer and Damian [4] showed that all YY6k for k ≥ 6 are spanners. Li and Zhan [23] generalized their result and proved that all even Yao-Yao graphs YY2k are spanners (for k ≥ 42). However, their technique cannot be extended to odd Yao-Yao graphs, and whether they are spanners are still elusive. In this paper, we show that, surprisingly, for any integer k ≥ 1, there exist odd Yao-Yao graph YY2k+1 instances, which are not spanners.
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Almost All Even Yao-Yao Graphs Are Spanners
It is an open problem whether Yao-Yao graphs YYk (also known as sparse-Yao graphs) are all spanners when the integer parameter k is large enough. In this paper we show that, for any integer k ≥ 42, the Yao-Yao graph YY2k is a tk-spanner, with stretch factor tk = 6.03 +O(k −1) when k tends to infinity. Our result generalizes the best known result which asserts that all YY6k are spanners for k ≥ ...
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