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The Slimming Number and Genus of Graphs

Published online by Cambridge University Press:  20 November 2018

Richard K. Guy
Richard K. Guy*
Affiliation:
University of Calgary, Calgary, Alberta
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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, e1e2,…, es, which must be removed from G in order that G—∪ ei be planar.

For the complete graph, Kn (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 K3, and adding points successively, joining them to the three vertices of the region in which they lie, so

1

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 15 , Issue 2 , June 1972 , pp. 195 - 200
Copyright
Copyright © Canadian Mathematical Society 1972

References

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