License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.49
URN: urn:nbn:de:0030-drops-87621
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Jin, Yifei ; Li, Jian ; Zhan, Wei

Odd Yao-Yao Graphs are Not Spanners

LIPIcs-SoCG-2018-49.pdf (2 MB)


It is a long standing open problem whether Yao-Yao graphs YY_{k} are all spanners [Li et al. 2002]. Bauer and Damian [Bauer and Damian, 2012] showed that all YY_{6k} for k >= 6 are spanners. Li and Zhan [Li and Zhan, 2016] generalized their result and proved that all even Yao-Yao graphs YY_{2k} 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 YY_{2k+1} instances, which are not spanners.

BibTeX - Entry

  author =	{Yifei Jin and Jian Li and Wei Zhan},
  title =	{{Odd Yao-Yao Graphs are Not Spanners}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{49:1--49:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-87621},
  doi =		{10.4230/LIPIcs.SoCG.2018.49},
  annote =	{Keywords: Odd Yao-Yao Graph, Spanner, Counterexample}

Keywords: Odd Yao-Yao Graph, Spanner, Counterexample
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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