Girth greater than 4

ex(n;4)
P.Erd&ouml;s conjectured that ex(n;4)=(1/2 + o(1))3/2 n3/2.

Garnick et al. demonstrated that extremal graphs include:
 * Stars K1,n-1 and Paths Pn for n ≤  4,
 * Moore graphs:
 * EX(5;4)={C5} the cycle;
 * ex(10;4)= 15 is attained by the Petersen graph ;
 * ex(50;4)=175 is attained by the Hoffman-Singleton graph;
 * ex(3250;4) is attained by the Moore graph with girth 5 and degree 57 if it exists.
 * C6 is an element of EX(6;4).
 * polarity graphs.

Let G be an extremal graph of order n. Then
 * 1) the diameter of G is at most 3;
 * 2) if d(x)=&delta;(G)=1, then the graph G-{x}'' has diameter at most 2.

The following table lists the known values and constructive lower bounds for ex(n;4). If the value is known then it is shown in bold text.

The following table is the key to the colors in the table presented above: