DIR Return Create A Forum - Home
       ---------------------------------------------------------
       knight tours
  HTML https://knighttours.createaforum.com
       ---------------------------------------------------------
       *****************************************************
   DIR Return to: toroidal tours
       *****************************************************
       #Post#: 48--------------------------------------------------
       edge-disjoint tours
   DIR By: gsgs
       Date: May 13, 2026, 6:53 pm
       ---------------------------------------------------------
       Alspach's Cayley graph conjecture from 1984 states:
       every connected 2k-regular Cayley graph
       of a finite abelian group has a Hamilton decomposition.
       It had been proved by xxx for k=2 in 1988
       and for k=3 in 2009 by EE Westlund, J Liu, DL Kreher
       -------------------------------------------
       4 edge-disjoint 8x8 toroidal closed knight's tours
       00,17,34,51,04,21,38,55,57,10,27,44,61,14,31,40,
       50,03,20,37,54,07,16,33,43,60,13,30,47,56,09,26,
       36,53,06,23,32,49,02,19,29,46,63,08,25,42,59,12,
       22,39,48,01,18,35,52,05,15,24,41,58,11,28,45,62
       56,41,26,11,60,45,30,15,01,50,35,20,05,54,39,16,
       10,59,44,29,14,63,40,25,19,04,53,38,23,00,49,34,
       28,13,62,47,24,09,58,43,37,22,07,48,33,18,03,52,
       46,31,08,57,42,27,12,61,55,32,17,02,51,36,21,06
       00,10,20,30,32,42,52,62,15,17,27,37,47,49,59,05,
       22,24,34,44,54,56,02,12,29,39,41,51,61,07,09,19,
       36,46,48,58,04,14,16,26,43,53,63,01,11,21,31,33,
       50,60,06,08,18,28,38,40,57,03,13,23,25,35,45,55
       56,50,44,38,24,18,12,06,55,41,35,29,23,09,03,61,
       46,32,26,20,14,00,58,52,37,31,17,11,05,63,49,43,
       28,22,08,02,60,54,40,34,19,13,07,57,51,45,39,25,
       10,04,62,48,42,36,30,16,01,59,53,47,33,27,21,06
       *****************************************************
       Page 1 of 1