Ex(n;5)

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 <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, ex_l(240;5)=1320, ex(266;5)=1596, ex_l(336;5)=2184, ex(366;5)=2562, ex_l(462;5)=3465, ex_l(504;5)=4032, ex(546;5)=4641, ex(614;5)=5526, ex_l(720;5)=6840 and ex(762;5)=7620.

References

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