# Ex(n;5)

From Combinatorics Wiki

Known values for ex(n;5)
n 0 1 2 3 4 5 6 7 8 9
0 0 0 1 2 3 4 6 7 9 10
10 12 14 16 18 21 22 24 26 29 31
20 34 36 39 42 45 48 52 53 56 58
30 61 64 67 70 74 77 81 84 88 92
40 96 100 105 106-108 108-112 110-116 114-119 118-123 122-127 125-131
50 130-135 134-139 138-143 142-147 147-151 151-155 156-160 160-164 165-168 170-172
60 175-177 180-181 186

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

 Color References * E. Abajo and A. Diánez E. Abajo, A. Diánez, Size of Graphs with High Girth, Electronic Notes in Discrete Mathematics 29 (2007) 179--183 * E. Abajo and A. Diánez E. Abajo, A. Diánez, Exact values of ex(v;{C3,C4,... , Cn}), Discrete Applied Mathematics 158 (2010) 1869--1878

In addition to the values shown in the table above, large graphs, constructed by researches interested in The Cage Problem, provide good constructive lower bounds for the extremal number. For example: ex(42;5)=105, ex(62;5)=186, ex(90;5)=315,ex(114;5)=456, ex(146;5)=657, ex(182;5)=910, exl(240;5)=1320, ex(266;5)=1596, exl(336;5)=2184, ex(366;5)=2562, exl(462;5)=3465, exl(504;5)=4032, ex(546;5)=4641, ex(614;5)=5526, exl(720;5)=6840 and ex(762;5)=7620.

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