Edge complexity of geometric graphs on convex independent point sets

Abhijeet Khopkar

Edge complexity of geometric graphs on convex independent point sets

Discrete Mathematics 2017-04-24 v2

Authors: Abhijeet Khopkar

Abstract

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 $O(n \log n)$ .

Keywords

geometric graphs convex independent point sets Locally Gabriel graphs unit distance graphs edge complexity graph bounds

Cite

@article{arxiv.1605.08066,
  title  = {Edge complexity of geometric graphs on convex independent point sets},
  author = {Abhijeet Khopkar},
  journal= {arXiv preprint arXiv:1605.08066},
  year   = {2017}
}

Comments

unit distance graph, convex point sets. arXiv admin note: substantial text overlap with arXiv:1312.2185

Edge complexity of geometric graphs on convex independent point sets

Abstract

Keywords

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