Longest uncrossed paths of fairy-chess leapers 

This table contains my best results, obtained by means of a heuristic pen and paper search supported by a brute force computer backtracking search.
I added the board coverage (ratio of visited/all possible fields) to detect possible weak results in a column but was not able to "flaten" all results.
My results on boards of odd sidelength are slightly better, because then the computer search uses mirror symmetry.
The longest path of every leaper seems to be arranged diagonally or laterally depending on the ablities of the token.

Pictures of longest path
Size of board Knight (1,2) Carpenter (1,2)+(0,2) Dragon (1,2)+(0,3) Frog (1,2)+(2,2) Gnu (1,2)+(1,3) (2,0)+(4,1)
6x6 picture
Length/coverage 17 / 47.2% 23 / 63.9% 19 / 52.8% 20 / 55.5% 27 / 75% 20 / 55.5%
7x7
Length/coverage 24 / 49% 32 / 65.3% 30 / 61.2% 30 / 61.2% 40 / 81.6% 28 /  57.14%
8x8
Length/coverage 35 / 54.7% 45 / 70.3% 37 / 57.8% 41 / 64% 54 / 84.4% 37 / 57.8%
9x9
Length/coverage 47 / 58% 58 / 71.6% 50 / 61.7% 56 / 69.13% 69 / 85.2% 50 / 61.7%
10x10
Length/coverage 61 / 61% 74 / 74% 65 / 65% 68 / 68% 85 / 85% 64 / 64%
11x11 76  
Length/coverage  76 / 62.8% 91 / 75.2% 81 / 66.9%  84 / 69.4 % 103 / 85.1% 80 / 66.1%
12x12 94  
Length/coverage 94/ 65.3% 110 / 76.4% 99 / 68.75% 99  / 68.75% 124 / 86.1% 95 / 65.97%

If you are able to improve any of the presented results, please contact me at alexanderfischer@hotmail.com.
I also wrote an android app, where one can explore uncrossed leaper paths manually. It can be found at Google play as "uncrossed knight tour ".
Besucherzaehler