Geodesic
The Slimming Number and Genus of Graphs
Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 195-200

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J. Ch. Boland suggested, and Mrs. Sheehan named, the idea of the slimming number of a graph G, i.e. the minimum number, s(G), of edges, e 1e 2,..., e s, which must be removed from G in order that G—∪ e i be planar.For the complete graph, K n (n≥3), it may be seen by Euler's formula that a planar subgraph contains at most 3n—6 edges; moreover one may construct such a subgraph inductively, starting from K 3, and adding points successively, joining them to the three vertices of the region in which they lie, so 1 
Guy, Richard K. The Slimming Number and Genus of Graphs. Canadian mathematical bulletin, Tome 15 (1972) no. 2, pp. 195-200. doi: 10.4153/CMB-1972-035-8
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     title = {The {Slimming} {Number} and {Genus} of {Graphs}},
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