On the maximum number of edges of non-flowerable coin graphs
نویسندگان
چکیده
For n ∈ N and 3 ≤ k ≤ n we compute the exact value of Ek(n), the maximum number of edges of a simple planar graph on n vertices where each vertex bounds an l-gon where l ≥ k. The lower bound of Ek(n) is obtained by explicit construction, and the matching upper bound is obtained by using Integer Programming (IP.) We then use this result to conjecture the maximum number of edges of a non-flowerable coin graph on n vertices. A flower is a coin graph representation of the wheel graph. A collection of coins or discs in the Euclidean plane is non-flowerable if no flower can be formed by coins from the collection. 2000 MSC: 05A15, 05C35.
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