Ex(n;5)
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Revision as of 06:00, 30 March 2011 by CW>KimMarshall
| 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 <ref>E. Abajo, A. Diánez, Size of Graphs with High Girth, Electronic Notes in Discrete Mathematics 29 (2007) 179--183</ref> |
| * | E. Abajo and A. Diánez <ref>E. Abajo, A. Diánez, Exact values of ex(v;{C3,C4,... , Cn}), Discrete Applied Mathematics 158 (2010) 1869--1878</ref> |
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
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