Types of 2-factorisations of <{1,2,3,4}>_{10}. Label 2-factor A C10 B C4C3C3 C C5C5 D C6C4 E C7C3 All possible types exist: AAAA (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,6,2,8,5,9,1,7,4) (0,6,4,8,1,5,2,9,3,7) AAAB (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,6,2,9,5,1,8,4,7) (1,7,3,9)(0,4,6)(2,5,8) AAAC (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,9,1,7,4,8,5,2,6) (0,4,6,3,7)(1,5,9,2,8) AAAD (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,8,6,9,7) (0,3,6,2,8,1,9,5,7,4) (1,5,2,9,3,7)(0,6,4,8) AAAE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,6,2,5,9,1,8,4,7) (1,5,8,2,9,3,7)(0,4,6) AABB (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,8,5,7,9,6,3) (0,6,4,8)(1,3,7)(2,5,9) (1,5,3,9)(0,4,7)(2,6,8) AABC (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,8,6,9,7) (1,7,4,8)(0,3,6)(2,5,9) (0,4,6,2,8)(1,5,7,3,9) AABD (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,6,9,7,5,8) (0,3,7,4)(1,5,9)(2,6,8) (0,6,4,8,1,7)(2,5,3,9) AABE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,6,9,7,5,8) (1,5,2,9)(0,3,7)(4,6,8) (0,4,7,1,8,2,6)(3,5,9) AACC (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,6,4,7)(1,8,5,2,9) (0,4,8,2,6)(1,5,9,3,7) AACD (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,6,4,7)(1,5,9,2,8) (0,4,8,5,2,6)(1,7,3,9) AACE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,8,6,9,7) (0,3,7,4,6)(1,5,9,2,8) (1,7,5,2,6,3,9)(0,4,8) AADD (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,7,5,9,6,8) (0,6,2,8,4,7)(1,5,3,9) (1,7,9,2,5,8)(0,3,6,4) AADE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,6,8,5,9,7) (0,3,5,7,4,6)(1,8,2,9) (1,5,2,6,9,3,7)(0,4,8) AAEE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,5,7,9,6,8) (0,3,6,2,8,4,7)(1,5,9) (1,7,3,9,2,5,8)(0,4,6) ABBB (0,1,2,3,4,5,7,6,9,8) (1,3,9,7)(0,4,6)(2,5,8) (1,4,7,8)(0,2,9)(3,5,6) (2,4,8,6)(0,3,7)(1,5,9) ABBC (0,1,2,3,4,5,6,7,9,8) (0,2,5,7)(1,3,9)(4,6,8) (0,3,7,4)(1,5,8)(2,6,9) (0,6,3,5,9)(1,4,2,8,7) ABBD (0,1,2,3,4,5,6,7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,3,1,4)(2,6,8)(5,7,9) (1,7,3,5,2,9)(0,6,4,8) ABBE (0,1,2,3,4,5,6,7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,6,4,8)(1,3,7)(2,5,9) (0,3,5,7,9,1,4)(2,6,8) ABCC (0,1,2,3,4,5,6,7,8,9) (0,2,5,7)(1,3,9)(4,6,8) (0,3,5,9,6)(1,7,4,2,8) (0,4,1,5,8)(2,6,3,7,9) ABCD (0,1,2,3,4,5,6,7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,4,6,2,8)(1,7,3,5,9) (0,3,1,4,8,6)(2,5,7,9) ABCE (0,1,2,3,4,5,6,7,8,9) (0,2,4,6)(1,5,8)(3,7,9) (0,3,1,4,7)(2,5,9,6,8) (1,7,5,3,6,2,9)(0,4,8) ABDD (0,1,2,3,4,5,6,7,8,9) (0,2,4,6)(1,5,8)(3,7,9) (0,3,5,7,1,4)(2,8,6,9) (1,3,6,2,5,9)(0,7,4,8) ABDE (0,1,2,3,4,5,6,7,8,9) (0,2,4,6)(1,5,8)(3,7,9) (0,4,8,2,5,7)(1,3,6,9) (0,3,5,9,2,6,8)(1,4,7) ABEE (0,1,2,3,4,5,6,7,8,9) (0,2,4,6)(1,5,8)(3,7,9) (0,3,5,7,1,4,8)(2,6,9) (1,3,6,8,2,5,9)(0,4,7) ACCC (0,1,2,3,4,5,6,7,9,8) (0,2,4,1,7)(3,6,8,5,9) (0,3,1,9,6)(2,5,7,4,8) (0,4,6,2,9)(1,5,3,7,8) ACCD (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,7)(3,6,8,5,9) (0,3,5,2,6)(1,8,4,7,9) (0,4,6,9,2,8)(1,3,7,5) ACCE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,3,7,4,6)(1,5,9,2,8) (1,3,6,2,5,7,9)(0,4,8) ACDD (0,1,2,3,4,5,6,7,8,9) (0,2,4,8,6)(1,5,3,7,9) (2,5,7,4,6,9)(0,3,1,8) (2,6,3,9,5,8)(0,4,1,7) ACDE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3)(5,7,9,6,8) (0,6,2,8,4,7)(1,5,3,9) (0,4,6,3,7,1,8)(2,5,9) ACEE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,7)(3,6,8,5,9) (0,3,1,5,7,4,8)(2,6,9) (1,8,2,5,3,7,9)(0,4,6) ADDD (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,7)(5,8,6,9) (0,3,6,2,8,4)(1,5,7,9) (0,6,4,7,1,8)(2,5,3,9) ADDE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,7)(5,8,6,9) (0,3,5,7,4,6)(1,8,2,9) (1,5,2,6,3,9,7)(0,4,8) ADEE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,5,8)(3,6,9,7) (0,3,1,9,2,5,7)(4,6,8) (0,4,7,1,8,2,6)(3,5,9) AEEE (0,1,2,3,4,5,6,7,8,9) (0,2,4,1,3,6,8)(5,7,9) (0,3,9,1,7,4,6)(2,5,8) (0,4,8,1,5,3,7)(2,6,9) BBBB (0,1,2,3)(4,5,7)(6,8,9) (0,2,4,6)(1,7,8)(3,5,9) (1,5,2,9)(0,4,8)(3,6,7) (2,6,5,8)(0,7,9)(1,3,4) BBBC (0,1,2,3)(4,5,6)(7,8,9) (0,2,6,8)(1,4,7)(3,5,9) (1,3,7,5)(0,6,9)(2,4,8) (0,4,3,6,7)(1,8,5,2,9) BBBD (0,1,2,3)(4,5,6)(7,8,9) (0,2,5,7)(1,4,8)(3,6,9) (0,6,2,8)(1,5,9)(3,4,7) (1,3,5,8,6,7)(0,4,2,9) BBBE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,4,1,9)(2,6,8)(3,5,7) (0,6,7,1,3,4,8)(2,5,9) BBCC (0,1,2,3)(4,5,6)(7,8,9) (0,2,5,8)(1,4,7)(3,6,9) (0,4,2,8,6)(1,3,7,5,9) (0,7,6,2,9)(1,5,3,4,8) BBCD (0,1,2,3)(4,5,6)(7,8,9) (0,2,5,8)(1,4,7)(3,6,9) (0,4,3,7,6)(1,5,9,2,8) (0,7,5,3,1,9)(2,4,8,6) BBCE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,4,8,2,6)(1,7,3,5,9) (0,8,6,7,5,2,9)(1,3,4) BBDD (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,8)(1,5,7)(3,6,9) (0,7,3,4,1,9)(2,5,8,6) (1,3,5,9,2,8)(0,4,7,6) BBDE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,6,8,2,5,9)(1,4,3,7) (1,3,5,7,6,2,9)(0,4,8) BBEE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,7)(1,5,8)(3,6,9) (0,4,3,1,7,6,8)(2,5,9) (0,6,2,8,4,1,9)(3,5,7) BCCC (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7)(3,6,8,5,9) (0,4,8,1,9)(2,5,3,7,6) (0,6,9,2,8)(1,3,4,7,5) BCCD (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,4,7,3,6)(1,5,9,2,8) (0,8,4,3,1,9)(2,5,7,6) BCCE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,4,8,2,9)(1,3,6,7,5) (0,6,2,5,9,1,8)(3,4,7) BCDD (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7)(3,6,8,5,9) (0,4,8,2,9,6)(1,3,7,5) (2,5,3,4,7,6)(0,8,1,9) BCDE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,6,7,5,2,9)(1,3,4,8) (0,4,7,3,6,2,8)(1,5,9) BCEE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,6,2,8,1,5,9)(3,4,7) (1,3,6,7,5,2,9)(0,4,8) BDDD (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,3,5,7)(1,8,6,9) (0,4,8,5,2,9)(1,3,6,7) (1,4,7,3,9,5)(0,6,2,8) BDDE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,3,7)(5,8,6,9) (0,6,2,8,1,9)(3,4,7,5) (1,5,2,9,3,6,7)(0,4,8) BDEE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,5,8)(3,7,6,9) (0,4,3,5,7,1,9)(2,6,8) (0,6,3,1,8,4,7)(2,5,9) BEEE (0,1,2,3)(4,5,6)(7,8,9) (0,2,4,1,7,5,8)(3,6,9) (0,4,7,3,1,5,9)(2,6,8) (1,8,4,3,5,2,9)(0,6,7) CCCC (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,8)(3,5,7,9,6) (0,3,7,1,9)(2,6,4,5,8) (0,6,8,4,7)(1,3,9,2,5) CCCD (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,3,6,2,9)(1,5,7,4,8) (0,6,4,5,2,8)(1,3,7,9) CCCE (0,1,2,3,4)(5,6,7,8,9) (0,2,4,5,7)(1,8,6,3,9) (0,3,1,5,8)(2,6,4,7,9) (1,4,8,2,5,3,7)(0,6,9) CCDD (0,1,2,3,4)(5,6,7,8,9) (0,2,4,5,7)(1,3,9,6,8) (0,3,6,2,5,8)(1,4,7,9) (0,6,4,8,2,9)(1,5,3,7) CCDE (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,7)(3,5,8,6,9) (0,8,1,3,7,9)(2,5,4,6) (1,5,7,4,8,2,9)(0,3,6) CCEE (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,8)(3,5,7,9,6) (0,3,7,1,5,2,9)(4,6,8) (0,6,2,8,5,4,7)(1,3,9) CDDD (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,7,9)(3,5,8,6) (0,3,7,5,4,6)(1,8,2,9) (1,3,9,6,2,5)(0,7,4,8) CDDE (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,9,7)(3,5,8,6) (0,6,4,7,3,9)(1,5,2,8) (0,3,1,7,5,4,8)(2,6,9) CDEE (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,5,8)(3,6,9,7) (0,3,5,2,9,1,7)(4,6,8) (0,6,2,8,1,3,9)(4,5,7) CEEE (0,1,2,3,4)(5,6,7,8,9) (0,2,4,1,7,5,8)(3,6,9) (0,6,2,8,4,7,9)(1,3,5) (1,8,6,4,5,2,9)(0,3,7) DDDD (0,1,2,3,4,6)(5,7,8,9) (0,2,4,1,7,9)(3,5,8,6) (0,3,7,6,5,4)(1,8,2,9) (1,3,9,6,2,5)(0,7,4,8) DDDE (0,1,2,3,4,6)(5,7,8,9) (0,2,4,1,5,8)(3,6,7,9) (0,3,1,8,4,7)(2,5,6,9) (0,4,5,3,7,1,9)(2,6,8) DDEE (0,1,2,3,4,6)(5,7,8,9) (0,2,4,1,5,8)(3,6,9,7) (1,3,5,6,8,2,9)(0,4,7) (1,7,6,2,5,4,8)(0,3,9) DEEE (0,1,2,3,4,6)(5,7,8,9) (0,2,4,1,3,9,7)(5,6,8) (0,3,5,1,7,4,8)(2,6,9) (0,4,5,2,8,1,9)(3,6,7) EEEE (0,1,2,3,4,5,6)(7,8,9) (0,2,4,1,7,5,8)(3,6,9) (0,3,1,8,4,6,7)(2,5,9) (0,4,7,3,5,1,9)(2,6,8)