Given a circle $C$ with known radius $r$, I want to determine the maximum number of nodes in the circle, where there is a distance constraint between each two nodes equal to $s$, i.e. each two nodes should have a distance equal or more than $s$.
I am searching for the solution on a network, but maybe it can be derived when the solution on a plane is available. By the solution on a network I mean the center of the circle is on a vertex, and the nodes can only be placed on vertices, as well.
Apparently the answer depends on the ratio of $s$ to $r$. But, is there a known formula to calculate such upper bound for nodes? if not, how I should approach the problem?