Corpus ID: 16469845

Edge complexity of geometric graphs on convex independent point sets

@article{Khopkar2016EdgeCO,
  title={Edge complexity of geometric graphs on convex independent point sets},
  author={A. Khopkar},
  journal={arXiv: Discrete Mathematics},
  year={2016}
}
  • A. Khopkar
  • Published 2016
  • Mathematics
  • arXiv: Discrete Mathematics
In this paper, we focus on a generalised version of Gabriel graphs known as Locally Gabriel graphs ($LGGs$) and Unit distance graphs ($UDGs$) on convexly independent point sets. $UDGs$ are sub graphs of $LGGs$. We give a simpler proof for the claim that $LGGs$ on convex independent point sets have $2n \log n + O(n)$ edges. Then we prove that unit distance graphs on convex independent point sets have $O(n)$ edges improving the previous known bound of $O(n \log n)$. 

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