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 [1]
* E. Abajo and A. Diánez [2]


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.

References

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