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arXiv · 1605.08066

Edge complexity of geometric graphs on convex independent point sets

Abhijeet Khopkar
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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 $O(n \log n)$.

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Abhijeet Khopkar. 2016-05-24. Edge complexity of geometric graphs on convex independent point sets. https://arxiv.org/abs/1605.08066

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