Ex(n;8)

From Combinatorics Wiki

Table of known values for ex(n;8).
n 0 1 2 3 4 5 6 7 8 9
0 0 0 1 2 3 4 5 6 8 9
10 10 11 12 14 15 16 18 19 21 22
20 23 25 27 28 29 31 33 34 35 37
30 39 40 42 43 45 47 48 50 52 54
40 55 57 58 60 62 64 65 67 69 71
50 73 75 77 78 80 81 83 85 87 88
60 90 91 93 95 97 99 100 102 103 105

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

Color References
* Folklore.
* Biggs and Hoare [1]
* Frucht [2]
* Abajo and Diánez [3]
* Marshall et al. [4]

References

  1. N. L. Biggs, M. J. Hoare, A trivalent graph with 58 vertices and girth 9, Discrete Mathematics 30 Issue 3 (1980) 299-301
  2. R. Frucht, Remarks on finite groups defined by generating relations, Canadian Journal Mathematics 7 (1955) 8-17
  3. E. Abajo, A. Diánez, Size of Graphs with High Girth, Electronic Notes in Discrete Mathematics 29 (2007) 179--183
  4. K. Marshall, M. Miller and J. Ryan, Extremal Graphs without Cycles of length 8 or less, preprint