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doi:10.1016/0012-365X(94)00190-T 
Copyright © 1995 Published by Elsevier Science B.V.
Size in maximal triangle-free graphs and minimal graphs of diameter 2
Received 7 July 1993;
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Abstract
A triangle-free graph is maximal if the addition of any edge creates a triangle. For n 
5, we show there is an n-nodem-edge maximal triangle-free graph if and only if it is complete bipartite or 2n − 5 
m 
(n − 1)2/4
+ 1. A diameter 2 graph is minimal if the deletion of any edge increases the diameter. We show that a triangle-free graph is maximal if and only if it is minimal of diameter 2.
For n> no where no is a vastly huge number, Füredi showed that an n-node nonbipartite minimal diameter 2 graph has at most (n − 1)2/4 + 1 edges. We demonstrate that n0 6 by producing a 6-node nonbipartite minimal diameter 2 graph with 8 edges.
Author Keywords: Maximal triangle-free; Minimal diameter 2
