It is a long standing open problem whether Yao-Yao graphs YY_{k} are all spanners ~\mbox{%DIFAUXCMD li2002sparse . Bauer and Damian ~\mbox{%DIFAUXCMD bauer2013infinite showed that all YY_{6k} for k \geq 6 are spanners. Li and Zhan ~\mbox{%DIFAUXCMD li2016almost generalized their result and proved that all even Yao-Yao graphs YY_{2k} are spanners (for k\geq 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 \geq 1, there exist odd Yao-Yao graph YY_{2k+1} instances, which are not spanners.
It is a long standing open problem whether Yao-Yao graphs YY_{k} are all spanners li2002sparse . Bauer and Damian bauer2013infinite showed that all YY_{6k} for k \geq 6 are spanners. Li and Zhan li2016almost generalized their result and proved that all even Yao-Yao graphs YY_{2k} are spanners (for k\geq 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 \geq 1, there exist odd Yao-Yao graph YY_{2k+1} instances, which are not spanners.
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~\mbox{%DIFAUXCMD li2002sparse
li2002sparse
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~\mbox{%DIFAUXCMD bauer2013infinite
bauer2013infinite
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~\mbox{%DIFAUXCMD li2016almost
li2016almost