==================================================================================================== 25 b r r b b r b b r b r b r b r b r r r r b r b r r 0 4 0 19 0 20 0 23 2 18 3 4 3 16 5 7 6 9 6 17 6 22 6 23 7 8 7 10 7 15 7 22 8 9 8 13 8 23 9 16 10 14 11 15 11 16 11 21 11 24 12 22 12 24 14 18 15 17 15 21 16 19 21 24 -1 +++ Original graph (G) [b] 0 -> 4, 19, 20, 23 [r] 1 -> [r] 2 -> 18 [b] 3 -> 4, 16 [b] 4 -> 0, 3 [r] 5 -> 7 [b] 6 -> 9, 17, 22, 23 [b] 7 -> 5, 8, 10, 15, 22 [r] 8 -> 7, 9, 13, 23 [b] 9 -> 6, 8, 16 [r] 10 -> 7, 14 [b] 11 -> 15, 16, 21, 24 [r] 12 -> 22, 24 [b] 13 -> 8 [r] 14 -> 10, 18 [b] 15 -> 7, 11, 17, 21 [r] 16 -> 3, 9, 11, 19 [r] 17 -> 6, 15 [r] 18 -> 2, 14 [r] 19 -> 0, 16 [b] 20 -> 0 [r] 21 -> 11, 15, 24 [b] 22 -> 6, 7, 12 [r] 23 -> 0, 6, 8 [r] 24 -> 11, 12, 21 +++ Red subgraph (GR) [r] 1 -> [r] 2 -> 18 [r] 5 -> [r] 8 -> 23 [r] 10 -> 14 [r] 12 -> 24 [r] 14 -> 10, 18 [r] 16 -> 19 [r] 17 -> [r] 18 -> 2, 14 [r] 19 -> 16 [r] 21 -> 24 [r] 23 -> 8 [r] 24 -> 12, 21 +++ Blue subgraph (GB) [b] 0 -> 4, 20 [b] 3 -> 4 [b] 4 -> 0, 3 [b] 6 -> 9, 22 [b] 7 -> 15, 22 [b] 9 -> 6 [b] 11 -> 15 [b] 13 -> [b] 15 -> 7, 11 [b] 20 -> 0 [b] 22 -> 6, 7 +++ Red cycles +++ Blue cycles +++ Nonmonochromatic graph (GRB) [b] 0 -> 23, 19, 20, 4 [r] 1 -> [r] 2 -> 18 [b] 3 -> 16, 4 [b] 4 -> 0, 3 [r] 5 -> 7 [b] 6 -> 23, 17, 22, 9 [b] 7 -> 10, 8, 5, 15, 22 [r] 8 -> 13, 9, 7, 23 [b] 9 -> 16, 8, 6 [r] 10 -> 7, 14 [b] 11 -> 24, 21, 16, 15 [r] 12 -> 22, 24 [b] 13 -> 8 [r] 14 -> 18, 10 [b] 15 -> 21, 17, 7, 11 [r] 16 -> 11, 9, 3, 19 [r] 17 -> 15, 6 [r] 18 -> 2, 14 [r] 19 -> 0, 16 [b] 20 -> 0 [r] 21 -> 15, 11, 24 [b] 22 -> 12, 6, 7 [r] 23 -> 6, 0, 8 [r] 24 -> 11, 12, 21 +++ Multi-color cycles (22, 12, 24, 11, 21, 15, 17, 6), Color: (b, r, r, b, r, b, r, b) (16, 9, 8, 7, 22, 12, 24, 11), Color: (r, b, r, b, b, r, r, b) (4, 3, 16, 9, 8, 7, 22, 12, 24, 11, 21, 15, 17, 6, 23, 0), Color: (b, b, r, b, r, b, b, r, r, b, r, b, r, b, r, b) (19, 16, 9, 8, 7, 22, 12, 24, 11, 21, 15, 17, 6, 23, 0), Color: (r, r, b, r, b, b, r, r, b, r, b, r, b, r, b) (9, 8, 7, 22, 12, 24, 11, 21, 15, 17, 6), Color: (b, r, b, b, r, r, b, r, b, r, b) (8, 7, 22, 12, 24, 11, 21, 15, 17, 6, 23), Color: (r, b, b, r, r, b, r, b, r, b, r) (7, 22, 12, 24, 11, 21, 15), Color: (b, b, r, r, b, r, b) (24, 11, 21), Color: (r, b, r) (11, 21, 15), Color: (b, r, b) ==================================================================================================== 25 b b r b b r r r r r b r b b b b r b r r b b r b r 0 19 1 5 1 20 1 23 2 3 2 11 2 23 3 6 4 16 4 22 6 8 7 11 7 17 9 16 9 18 10 20 10 23 14 22 17 19 19 22 -1 +++ Original graph (G) [b] 0 -> 19 [b] 1 -> 5, 20, 23 [r] 2 -> 3, 11, 23 [b] 3 -> 2, 6 [b] 4 -> 16, 22 [r] 5 -> 1 [r] 6 -> 3, 8 [r] 7 -> 11, 17 [r] 8 -> 6 [r] 9 -> 16, 18 [b] 10 -> 20, 23 [r] 11 -> 2, 7 [b] 12 -> [b] 13 -> [b] 14 -> 22 [b] 15 -> [r] 16 -> 4, 9 [b] 17 -> 7, 19 [r] 18 -> 9 [r] 19 -> 0, 17, 22 [b] 20 -> 1, 10 [b] 21 -> [r] 22 -> 4, 14, 19 [b] 23 -> 1, 2, 10 [r] 24 -> +++ Red subgraph (GR) [r] 2 -> 11 [r] 5 -> [r] 6 -> 8 [r] 7 -> 11 [r] 8 -> 6 [r] 9 -> 16, 18 [r] 11 -> 2, 7 [r] 16 -> 9 [r] 18 -> 9 [r] 19 -> 22 [r] 22 -> 19 [r] 24 -> +++ Blue subgraph (GB) [b] 0 -> [b] 1 -> 20, 23 [b] 3 -> [b] 4 -> [b] 10 -> 20, 23 [b] 12 -> [b] 13 -> [b] 14 -> [b] 15 -> [b] 17 -> [b] 20 -> 1, 10 [b] 21 -> [b] 23 -> 1, 10 +++ Red cycles +++ Blue cycles (23, 10, 20, 1), Color: (b, b, b, b) +++ Nonmonochromatic graph (GRB) [b] 0 -> 19 [b] 1 -> 5, 20 [r] 2 -> 23, 3, 11 [b] 3 -> 6, 2 [b] 4 -> 22, 16 [r] 5 -> 1 [r] 6 -> 3, 8 [r] 7 -> 17, 11 [r] 8 -> 6 [r] 9 -> 18, 16 [b] 10 -> 23, 20 [r] 11 -> 2, 7 [b] 12 -> [b] 13 -> [b] 14 -> 22 [b] 15 -> [r] 16 -> 4, 9 [b] 17 -> 19, 7 [r] 18 -> 9 [r] 19 -> 17, 0, 22 [b] 20 -> 1, 10 [b] 21 -> [r] 22 -> 14, 4, 19 [b] 23 -> 2, 10 [r] 24 -> +++ Multi-color cycles ==================================================================================================== 25 b b b b b r b r b r r r r r b b b r r b b b r r b 0 2 0 14 0 18 1 14 2 4 3 4 3 20 4 20 4 23 5 9 5 11 5 12 7 15 7 21 8 23 9 12 9 13 9 15 9 18 10 23 11 14 11 17 16 20 17 18 19 20 19 24 21 23 22 24 -1 +++ Original graph (G) [b] 0 -> 2, 14, 18 [b] 1 -> 14 [b] 2 -> 0, 4 [b] 3 -> 4, 20 [b] 4 -> 2, 3, 20, 23 [r] 5 -> 9, 11, 12 [b] 6 -> [r] 7 -> 15, 21 [b] 8 -> 23 [r] 9 -> 5, 12, 13, 15, 18 [r] 10 -> 23 [r] 11 -> 5, 14, 17 [r] 12 -> 5, 9 [r] 13 -> 9 [b] 14 -> 0, 1, 11 [b] 15 -> 7, 9 [b] 16 -> 20 [r] 17 -> 11, 18 [r] 18 -> 0, 9, 17 [b] 19 -> 20, 24 [b] 20 -> 3, 4, 16, 19 [b] 21 -> 7, 23 [r] 22 -> 24 [r] 23 -> 4, 8, 10, 21 [b] 24 -> 19, 22 +++ Red subgraph (GR) [r] 5 -> 9, 11, 12 [r] 7 -> [r] 9 -> 5, 12, 13, 18 [r] 10 -> 23 [r] 11 -> 5, 17 [r] 12 -> 5, 9 [r] 13 -> 9 [r] 17 -> 11, 18 [r] 18 -> 9, 17 [r] 22 -> [r] 23 -> 10 +++ Blue subgraph (GB) [b] 0 -> 2, 14 [b] 1 -> 14 [b] 2 -> 0, 4 [b] 3 -> 4, 20 [b] 4 -> 2, 3, 20 [b] 6 -> [b] 8 -> [b] 14 -> 0, 1 [b] 15 -> [b] 16 -> 20 [b] 19 -> 20, 24 [b] 20 -> 3, 4, 16, 19 [b] 21 -> [b] 24 -> 19 +++ Red cycles (12, 9, 5), Color: (r, r, r) (11, 17, 18, 9, 5), Color: (r, r, r, r, r) +++ Blue cycles (20, 3, 4), Color: (b, b, b) +++ Nonmonochromatic graph (GRB) [b] 0 -> 18, 14, 2 [b] 1 -> 14 [b] 2 -> 4, 0 [b] 3 -> 20, 4 [b] 4 -> 23, 2, 3 [r] 5 -> 9 [b] 6 -> [r] 7 -> 21, 15 [b] 8 -> 23 [r] 9 -> 15, 18, 13, 12, 5 [r] 10 -> 23 [r] 11 -> 14, 17 [r] 12 -> 9 [r] 13 -> 9 [b] 14 -> 11, 0, 1 [b] 15 -> 9, 7 [b] 16 -> 20 [r] 17 -> 18, 11 [r] 18 -> 0, 9, 17 [b] 19 -> 24, 20 [b] 20 -> 3, 19, 16 [b] 21 -> 23, 7 [r] 22 -> 24 [r] 23 -> 21, 8, 4, 10 [b] 24 -> 22, 19 +++ Multi-color cycles (2, 4, 23, 21, 7, 15, 9, 18, 0), Color: (b, b, r, b, r, b, r, r, b) (14, 11, 17, 18, 0), Color: (b, r, r, r, b) ==================================================================================================== 25 b b b r b r b r b r r b b r r r r r r r b r r r r 0 4 0 8 0 15 0 20 1 21 2 11 3 11 4 7 4 13 5 9 5 13 5 23 6 12 7 9 7 10 7 16 7 19 7 20 7 24 9 16 9 18 9 19 9 20 10 14 10 19 12 16 12 20 12 24 14 21 14 22 14 23 15 17 17 21 18 19 18 20 18 21 18 24 19 21 20 21 -1 +++ Original graph (G) [b] 0 -> 4, 8, 15, 20 [b] 1 -> 21 [b] 2 -> 11 [r] 3 -> 11 [b] 4 -> 0, 7, 13 [r] 5 -> 9, 13, 23 [b] 6 -> 12 [r] 7 -> 4, 9, 10, 16, 19, 20, 24 [b] 8 -> 0 [r] 9 -> 5, 7, 16, 18, 19, 20 [r] 10 -> 7, 14, 19 [b] 11 -> 2, 3 [b] 12 -> 6, 16, 20, 24 [r] 13 -> 4, 5 [r] 14 -> 10, 21, 22, 23 [r] 15 -> 0, 17 [r] 16 -> 7, 9, 12 [r] 17 -> 15, 21 [r] 18 -> 9, 19, 20, 21, 24 [r] 19 -> 7, 9, 10, 18, 21 [b] 20 -> 0, 7, 9, 12, 18, 21 [r] 21 -> 1, 14, 17, 18, 19, 20 [r] 22 -> 14 [r] 23 -> 5, 14 [r] 24 -> 7, 12, 18 +++ Red subgraph (GR) [r] 3 -> [r] 5 -> 9, 13, 23 [r] 7 -> 9, 10, 16, 19, 24 [r] 9 -> 5, 7, 16, 18, 19 [r] 10 -> 7, 14, 19 [r] 13 -> 5 [r] 14 -> 10, 21, 22, 23 [r] 15 -> 17 [r] 16 -> 7, 9 [r] 17 -> 15, 21 [r] 18 -> 9, 19, 21, 24 [r] 19 -> 7, 9, 10, 18, 21 [r] 21 -> 14, 17, 18, 19 [r] 22 -> 14 [r] 23 -> 5, 14 [r] 24 -> 7, 18 +++ Blue subgraph (GB) [b] 0 -> 4, 8, 20 [b] 1 -> [b] 2 -> 11 [b] 4 -> 0 [b] 6 -> 12 [b] 8 -> 0 [b] 11 -> 2 [b] 12 -> 6, 20 [b] 20 -> 0, 12 +++ Red cycles (18, 21, 14, 10, 7, 9), Color: (r, r, r, r, r, r) (19, 18, 21, 14, 10, 7), Color: (r, r, r, r, r, r) (19, 18, 21, 14, 10, 7, 9), Color: (r, r, r, r, r, r, r) (19, 18, 21, 14, 10), Color: (r, r, r, r, r) (19, 18, 21), Color: (r, r, r) (24, 18, 21, 14, 10, 7), Color: (r, r, r, r, r, r) (23, 14, 10, 7, 9, 5), Color: (r, r, r, r, r, r) (16, 7, 9), Color: (r, r, r) +++ Blue cycles +++ Nonmonochromatic graph (GRB) [b] 0 -> 15, 20, 8, 4 [b] 1 -> 21 [b] 2 -> 11 [r] 3 -> 11 [b] 4 -> 13, 7, 0 [r] 5 -> 13, 9 [b] 6 -> 12 [r] 7 -> 20, 4, 16, 10, 9 [b] 8 -> 0 [r] 9 -> 20, 5, 7 [r] 10 -> 14, 7 [b] 11 -> 3, 2 [b] 12 -> 24, 16, 20, 6 [r] 13 -> 4, 5 [r] 14 -> 23, 22, 21, 10 [r] 15 -> 0, 17 [r] 16 -> 12, 7 [r] 17 -> 21, 15 [r] 18 -> 20, 24, 19, 21 [r] 19 -> 18 [b] 20 -> 21, 18, 9, 7, 0, 12 [r] 21 -> 20, 1, 14, 18, 17 [r] 22 -> 14 [r] 23 -> 14 [r] 24 -> 12, 18 +++ Multi-color cycles (7, 16, 12, 24, 18, 20), Color: (r, r, b, r, r, b) (9, 5, 13, 4, 7, 16, 12, 24, 18, 20), Color: (r, r, r, b, r, r, b, r, r, b) (9, 5, 13, 4, 7), Color: (r, r, r, b, r) (4, 7, 16, 12, 24, 18, 20, 21, 17, 15, 0), Color: (b, r, r, b, r, r, b, r, r, r, b) (14, 10, 7, 16, 12, 24, 18, 20, 21), Color: (r, r, r, r, b, r, r, b, r) (12, 24, 18, 20), Color: (b, r, r, b) (18, 20, 21), Color: (r, b, r) (20, 21, 17, 15, 0), Color: (b, r, r, r, b) ==================================================================================================== 32 r r r r b b r r b r r r b b r b b b b b r b r b b b r r r r b b 0 5 0 8 0 16 1 5 1 9 1 16 1 21 2 23 2 30 2 31 3 5 3 13 3 28 4 5 4 10 4 14 4 17 5 7 5 8 5 24 7 14 7 16 7 26 8 12 8 23 8 28 9 22 9 26 10 15 11 21 11 23 12 13 12 14 12 24 13 14 13 15 13 19 13 25 13 26 14 15 14 17 14 20 14 24 15 25 15 26 16 28 17 23 18 21 18 24 18 25 19 25 19 31 20 24 20 31 21 29 25 30 25 31 27 28 28 29 -1 +++ Original graph (G) [r] 0 -> 5, 8, 16 [r] 1 -> 5, 9, 16, 21 [r] 2 -> 23, 30, 31 [r] 3 -> 5, 13, 28 [b] 4 -> 5, 10, 14, 17 [b] 5 -> 0, 1, 3, 4, 7, 8, 24 [r] 6 -> [r] 7 -> 5, 14, 16, 26 [b] 8 -> 0, 5, 12, 23, 28 [r] 9 -> 1, 22, 26 [r] 10 -> 4, 15 [r] 11 -> 21, 23 [b] 12 -> 8, 13, 14, 24 [b] 13 -> 3, 12, 14, 15, 19, 25, 26 [r] 14 -> 4, 7, 12, 13, 15, 17, 20, 24 [b] 15 -> 10, 13, 14, 25, 26 [b] 16 -> 0, 1, 7, 28 [b] 17 -> 4, 14, 23 [b] 18 -> 21, 24, 25 [b] 19 -> 13, 25, 31 [r] 20 -> 14, 24, 31 [b] 21 -> 1, 11, 18, 29 [r] 22 -> 9 [b] 23 -> 2, 8, 11, 17 [b] 24 -> 5, 12, 14, 18, 20 [b] 25 -> 13, 15, 18, 19, 30, 31 [r] 26 -> 7, 9, 13, 15 [r] 27 -> 28 [r] 28 -> 3, 8, 16, 27, 29 [r] 29 -> 21, 28 [b] 30 -> 2, 25 [b] 31 -> 2, 19, 20, 25 +++ Red subgraph (GR) [r] 0 -> [r] 1 -> 9 [r] 2 -> [r] 3 -> 28 [r] 6 -> [r] 7 -> 14, 26 [r] 9 -> 1, 22, 26 [r] 10 -> [r] 11 -> [r] 14 -> 7, 20 [r] 20 -> 14 [r] 22 -> 9 [r] 26 -> 7, 9 [r] 27 -> 28 [r] 28 -> 3, 27, 29 [r] 29 -> 28 +++ Blue subgraph (GB) [b] 4 -> 5, 17 [b] 5 -> 4, 8, 24 [b] 8 -> 5, 12, 23 [b] 12 -> 8, 13, 24 [b] 13 -> 12, 15, 19, 25 [b] 15 -> 13, 25 [b] 16 -> [b] 17 -> 4, 23 [b] 18 -> 21, 24, 25 [b] 19 -> 13, 25, 31 [b] 21 -> 18 [b] 23 -> 8, 17 [b] 24 -> 5, 12, 18 [b] 25 -> 13, 15, 18, 19, 30, 31 [b] 30 -> 25 [b] 31 -> 19, 25 +++ Red cycles +++ Blue cycles (25, 15, 13), Color: (b, b, b) (24, 18, 25, 15, 13, 12, 8, 5), Color: (b, b, b, b, b, b, b, b) (24, 18, 25, 15, 13, 12), Color: (b, b, b, b, b, b) (19, 25, 15, 13), Color: (b, b, b, b) (31, 19, 25), Color: (b, b, b) (17, 23, 8, 5, 4), Color: (b, b, b, b, b) +++ Nonmonochromatic graph (GRB) [r] 0 -> 16, 8, 5 [r] 1 -> 21, 16, 5, 9 [r] 2 -> 31, 30, 23 [r] 3 -> 13, 5, 28 [b] 4 -> 14, 10, 5 [b] 5 -> 7, 3, 1, 0, 8, 4 [r] 6 -> [r] 7 -> 16, 5, 14, 26 [b] 8 -> 28, 0, 23, 12, 5 [r] 9 -> 26, 22, 1 [r] 10 -> 15, 4 [r] 11 -> 23, 21 [b] 12 -> 14, 13, 8 [b] 13 -> 26, 14, 3, 15, 12 [r] 14 -> 24, 17, 15, 13, 12, 4, 20, 7 [b] 15 -> 26, 14, 10, 25, 13 [b] 16 -> 28, 7, 1, 0 [b] 17 -> 14, 23 [b] 18 -> 24, 21, 25 [b] 19 -> 31, 25 [r] 20 -> 31, 24, 14 [b] 21 -> 29, 11, 1, 18 [r] 22 -> 9 [b] 23 -> 11, 2, 8, 17 [b] 24 -> 20, 14, 18 [b] 25 -> 30, 15, 19, 18 [r] 26 -> 15, 13, 9, 7 [r] 27 -> 28 [r] 28 -> 16, 8, 29, 3, 27 [r] 29 -> 21, 28 [b] 30 -> 2, 25 [b] 31 -> 20, 2, 19 +++ Multi-color cycles (8, 28, 16, 0), Color: (b, r, b, r) (29, 21, 11, 23, 8, 28), Color: (r, b, r, b, b, r) (1, 21, 11, 23, 8, 28, 16), Color: (r, b, r, b, b, r, b) (7, 5, 1, 21, 11, 23, 8, 28, 16), Color: (r, b, r, b, r, b, b, r, b) (13, 26, 15, 25, 30, 2, 31, 20, 24, 14), Color: (b, r, b, b, b, r, b, r, b, r) (3, 13, 26, 15, 25, 30, 2, 31, 20, 24, 14, 7, 5), Color: (r, b, r, b, b, b, r, b, r, b, r, r, b) (3, 13, 26, 15, 25, 30, 2, 31, 20, 24, 14, 7, 5, 1, 21, 11, 23, 8, 28), Color: (r, b, r, b, b, b, r, b, r, b, r, r, b, r, b, r, b, b, r) (13, 26, 15), Color: (b, r, b) (12, 13, 26, 15, 25, 30, 2, 31, 20, 24, 14), Color: (b, b, r, b, b, b, r, b, r, b, r) (12, 13, 26, 15, 25, 30, 2, 31, 20, 24, 14, 7, 5, 1, 21, 11, 23, 8), Color: (b, b, r, b, b, b, r, b, r, b, r, r, b, r, b, r, b, b) (9, 26, 15, 25, 30, 2, 31, 20, 24, 14, 7, 5, 1), Color: (r, r, b, b, b, r, b, r, b, r, r, b, r) (26, 15, 25, 30, 2, 31, 20, 24, 14, 7), Color: (r, b, b, b, r, b, r, b, r, r) (15, 25, 30, 2, 31, 20, 24, 14), Color: (b, b, b, r, b, r, b, r) (4, 10, 15, 25, 30, 2, 31, 20, 24, 14), Color: (b, r, b, b, b, r, b, r, b, r) (4, 10, 15, 25, 30, 2, 31, 20, 24, 14, 7, 5), Color: (b, r, b, b, b, r, b, r, b, r, r, b) (19, 25, 30, 2, 31), Color: (b, b, b, r, b) (18, 25, 30, 2, 31, 20, 24), Color: (b, b, b, r, b, r, b) (18, 25, 30, 2, 31, 20, 24, 14, 7, 5, 1, 21), Color: (b, b, b, r, b, r, b, r, r, b, r, b) (2, 31, 20, 24, 14, 7, 5, 1, 21, 11, 23), Color: (r, b, r, b, r, r, b, r, b, r, b) (20, 24, 14), Color: (r, b, r) (17, 14, 7, 5, 1, 21, 11, 23), Color: (b, r, r, b, r, b, r, b) (5, 1, 21, 11, 23, 8, 28, 16, 0), Color: (b, r, b, r, b, b, r, b, r) (5, 1, 21, 11, 23, 8), Color: (b, r, b, r, b, b) ==================================================================================================== 64 r b b r b r b r b r b r r r r r b b r r b b b b r r b r r b b b b b r b r r r b b r r r b b r r r b b r b r r r b r b r r r r r 0 17 0 30 0 45 0 48 0 56 1 17 1 34 2 18 2 38 2 56 2 61 3 12 3 24 3 34 3 47 3 62 4 54 5 22 5 46 5 57 5 59 5 63 7 57 9 42 9 47 11 19 11 53 12 44 12 49 13 18 13 30 13 44 13 46 13 55 13 58 13 60 13 61 15 40 16 22 16 42 16 46 18 19 18 25 19 39 19 59 20 42 21 44 22 39 23 26 23 34 23 44 25 43 25 61 26 47 27 38 28 33 28 36 29 46 31 40 32 63 34 49 37 56 38 58 40 57 44 48 46 52 49 61 -1 +++ Original graph (G) [r] 0 -> 17, 30, 45, 48, 56 [b] 1 -> 17, 34 [b] 2 -> 18, 38, 56, 61 [r] 3 -> 12, 24, 34, 47, 62 [b] 4 -> 54 [r] 5 -> 22, 46, 57, 59, 63 [b] 6 -> [r] 7 -> 57 [b] 8 -> [r] 9 -> 42, 47 [b] 10 -> [r] 11 -> 19, 53 [r] 12 -> 3, 44, 49 [r] 13 -> 18, 30, 44, 46, 55, 58, 60, 61 [r] 14 -> [r] 15 -> 40 [b] 16 -> 22, 42, 46 [b] 17 -> 0, 1 [r] 18 -> 2, 13, 19, 25 [r] 19 -> 11, 18, 39, 59 [b] 20 -> 42 [b] 21 -> 44 [b] 22 -> 5, 16, 39 [b] 23 -> 26, 34, 44 [r] 24 -> 3 [r] 25 -> 18, 43, 61 [b] 26 -> 23, 47 [r] 27 -> 38 [r] 28 -> 33, 36 [b] 29 -> 46 [b] 30 -> 0, 13 [b] 31 -> 40 [b] 32 -> 63 [b] 33 -> 28 [r] 34 -> 1, 3, 23, 49 [b] 35 -> [r] 36 -> 28 [r] 37 -> 56 [r] 38 -> 2, 27, 58 [b] 39 -> 19, 22 [b] 40 -> 15, 31, 57 [r] 41 -> [r] 42 -> 9, 16, 20 [r] 43 -> 25 [b] 44 -> 12, 13, 21, 23, 48 [b] 45 -> 0 [r] 46 -> 5, 13, 16, 29, 52 [r] 47 -> 3, 9, 26 [r] 48 -> 0, 44 [b] 49 -> 12, 34, 61 [b] 50 -> [r] 51 -> [b] 52 -> 46 [r] 53 -> 11 [r] 54 -> 4 [r] 55 -> 13 [b] 56 -> 0, 2, 37 [r] 57 -> 5, 7, 40 [b] 58 -> 13, 38 [r] 59 -> 5, 19 [r] 60 -> 13 [r] 61 -> 2, 13, 25, 49 [r] 62 -> 3 [r] 63 -> 5, 32 +++ Red subgraph (GR) [r] 0 -> 48 [r] 3 -> 12, 24, 34, 47, 62 [r] 5 -> 46, 57, 59, 63 [r] 7 -> 57 [r] 9 -> 42, 47 [r] 11 -> 19, 53 [r] 12 -> 3 [r] 13 -> 18, 46, 55, 60, 61 [r] 14 -> [r] 15 -> [r] 18 -> 13, 19, 25 [r] 19 -> 11, 18, 59 [r] 24 -> 3 [r] 25 -> 18, 43, 61 [r] 27 -> 38 [r] 28 -> 36 [r] 34 -> 3 [r] 36 -> 28 [r] 37 -> [r] 38 -> 27 [r] 41 -> [r] 42 -> 9 [r] 43 -> 25 [r] 46 -> 5, 13 [r] 47 -> 3, 9 [r] 48 -> 0 [r] 51 -> [r] 53 -> 11 [r] 54 -> [r] 55 -> 13 [r] 57 -> 5, 7 [r] 59 -> 5, 19 [r] 60 -> 13 [r] 61 -> 13, 25 [r] 62 -> 3 [r] 63 -> 5 +++ Blue subgraph (GB) [b] 1 -> 17 [b] 2 -> 56 [b] 4 -> [b] 6 -> [b] 8 -> [b] 10 -> [b] 16 -> 22 [b] 17 -> 1 [b] 20 -> [b] 21 -> 44 [b] 22 -> 16, 39 [b] 23 -> 26, 44 [b] 26 -> 23 [b] 29 -> [b] 30 -> [b] 31 -> 40 [b] 32 -> [b] 33 -> [b] 35 -> [b] 39 -> 22 [b] 40 -> 31 [b] 44 -> 21, 23 [b] 45 -> [b] 49 -> [b] 50 -> [b] 52 -> [b] 56 -> 2 [b] 58 -> +++ Red cycles (59, 19, 18, 13, 46, 5), Color: (r, r, r, r, r, r) (61, 25, 18, 13), Color: (r, r, r, r) +++ Blue cycles +++ Nonmonochromatic graph (GRB) [r] 0 -> 56, 45, 30, 17, 48 [b] 1 -> 34, 17 [b] 2 -> 61, 38, 18, 56 [r] 3 -> 62, 47, 34, 24, 12 [b] 4 -> 54 [r] 5 -> 22, 63, 57, 46 [b] 6 -> [r] 7 -> 57 [b] 8 -> [r] 9 -> 42, 47 [b] 10 -> [r] 11 -> 53, 19 [r] 12 -> 49, 44, 3 [r] 13 -> 58, 44, 30, 60, 55, 18, 46 [r] 14 -> [r] 15 -> 40 [b] 16 -> 46, 42, 22 [b] 17 -> 0, 1 [r] 18 -> 2, 25, 19, 13 [r] 19 -> 39, 59, 18, 11 [b] 20 -> 42 [b] 21 -> 44 [b] 22 -> 5, 39, 16 [b] 23 -> 34, 26, 44 [r] 24 -> 3 [r] 25 -> 61, 43, 18 [b] 26 -> 47, 23 [r] 27 -> 38 [r] 28 -> 33, 36 [b] 29 -> 46 [b] 30 -> 13, 0 [b] 31 -> 40 [b] 32 -> 63 [b] 33 -> 28 [r] 34 -> 49, 23, 1, 3 [b] 35 -> [r] 36 -> 28 [r] 37 -> 56 [r] 38 -> 58, 2, 27 [b] 39 -> 19, 22 [b] 40 -> 57, 15, 31 [r] 41 -> [r] 42 -> 20, 16, 9 [r] 43 -> 25 [b] 44 -> 48, 13, 12, 21, 23 [b] 45 -> 0 [r] 46 -> 52, 29, 16, 5, 13 [r] 47 -> 26, 3, 9 [r] 48 -> 44, 0 [b] 49 -> 61, 34, 12 [b] 50 -> [r] 51 -> [b] 52 -> 46 [r] 53 -> 11 [r] 54 -> 4 [r] 55 -> 13 [b] 56 -> 37, 0, 2 [r] 57 -> 40, 5, 7 [b] 58 -> 38, 13 [r] 59 -> 19 [r] 60 -> 13 [r] 61 -> 49, 2, 25 [r] 62 -> 3 [r] 63 -> 32, 5 +++ Multi-color cycles (3, 47, 26, 23, 34), Color: (r, r, b, b, r) (12, 3, 47, 26, 23, 34, 49), Color: (r, r, r, b, b, r, b) (48, 44, 12, 3, 47, 26, 23, 34, 49, 61, 2, 56, 0), Color: (r, b, r, r, r, b, b, r, b, r, b, b, r) (38, 58, 13, 44, 12, 3, 47, 26, 23, 34, 49, 61, 2), Color: (r, b, r, b, r, r, r, b, b, r, b, r, b) (30, 13, 44, 12, 3, 47, 26, 23, 34, 49, 61, 2, 56, 0), Color: (b, r, b, r, r, r, b, b, r, b, r, b, b, r) (18, 13, 44, 12, 3, 47, 26, 23, 34, 49, 61, 2), Color: (r, r, b, r, r, r, b, b, r, b, r, b) (25, 18, 13, 44, 12, 3, 47, 26, 23, 34, 49, 61), Color: (r, r, r, b, r, r, r, b, b, r, b, r) (9, 42, 16, 46, 5, 22, 39, 19, 18, 13, 44, 12, 3, 47), Color: (r, r, b, r, r, b, b, r, r, r, b, r, r, r) (16, 46, 5, 22), Color: (b, r, r, b) (46, 5, 22, 39, 19, 18, 13), Color: (r, r, b, b, r, r, r) (44, 12, 3, 47, 26, 23), Color: (b, r, r, r, b, b) (17, 1, 34, 49, 61, 2, 56, 0), Color: (b, b, r, b, r, b, b, r) ==================================================================================================== 64 b r b r b r b b r b r r b r r b b b b r r r r b r r r b b r r b b b r r r b r b b r b b b r r b b r r r b b r b r b b r b r r b 0 6 1 33 2 4 2 46 3 46 3 49 4 25 5 57 5 62 6 39 7 9 7 24 8 55 9 51 11 57 12 26 16 27 16 35 16 48 16 60 17 22 19 36 19 49 20 54 21 61 21 62 22 32 22 45 22 52 22 53 23 24 24 35 25 60 26 27 26 37 26 43 26 44 27 59 28 46 28 47 29 49 33 60 37 52 38 39 38 41 39 49 41 54 42 45 42 46 43 62 50 59 54 57 56 57 57 60 57 61 -1 +++ Original graph (G) [b] 0 -> 6 [r] 1 -> 33 [b] 2 -> 4, 46 [r] 3 -> 46, 49 [b] 4 -> 2, 25 [r] 5 -> 57, 62 [b] 6 -> 0, 39 [b] 7 -> 9, 24 [r] 8 -> 55 [b] 9 -> 7, 51 [r] 10 -> [r] 11 -> 57 [b] 12 -> 26 [r] 13 -> [r] 14 -> [b] 15 -> [b] 16 -> 27, 35, 48, 60 [b] 17 -> 22 [b] 18 -> [r] 19 -> 36, 49 [r] 20 -> 54 [r] 21 -> 61, 62 [r] 22 -> 17, 32, 45, 52, 53 [b] 23 -> 24 [r] 24 -> 7, 23, 35 [r] 25 -> 4, 60 [r] 26 -> 12, 27, 37, 43, 44 [b] 27 -> 16, 26, 59 [b] 28 -> 46, 47 [r] 29 -> 49 [r] 30 -> [b] 31 -> [b] 32 -> 22 [b] 33 -> 1, 60 [r] 34 -> [r] 35 -> 16, 24 [r] 36 -> 19 [b] 37 -> 26, 52 [r] 38 -> 39, 41 [b] 39 -> 6, 38, 49 [b] 40 -> [r] 41 -> 38, 54 [b] 42 -> 45, 46 [b] 43 -> 26, 62 [b] 44 -> 26 [r] 45 -> 22, 42 [r] 46 -> 2, 3, 28, 42 [b] 47 -> 28 [b] 48 -> 16 [r] 49 -> 3, 19, 29, 39 [r] 50 -> 59 [r] 51 -> 9 [b] 52 -> 22, 37 [b] 53 -> 22 [r] 54 -> 20, 41, 57 [b] 55 -> 8 [r] 56 -> 57 [b] 57 -> 5, 11, 54, 56, 60, 61 [b] 58 -> [r] 59 -> 27, 50 [b] 60 -> 16, 25, 33, 57 [r] 61 -> 21, 57 [r] 62 -> 5, 21, 43 [b] 63 -> +++ Red subgraph (GR) [r] 1 -> [r] 3 -> 46, 49 [r] 5 -> 62 [r] 8 -> [r] 10 -> [r] 11 -> [r] 13 -> [r] 14 -> [r] 19 -> 36, 49 [r] 20 -> 54 [r] 21 -> 61, 62 [r] 22 -> 45 [r] 24 -> 35 [r] 25 -> [r] 26 -> [r] 29 -> 49 [r] 30 -> [r] 34 -> [r] 35 -> 24 [r] 36 -> 19 [r] 38 -> 41 [r] 41 -> 38, 54 [r] 45 -> 22 [r] 46 -> 3 [r] 49 -> 3, 19, 29 [r] 50 -> 59 [r] 51 -> [r] 54 -> 20, 41 [r] 56 -> [r] 59 -> 50 [r] 61 -> 21 [r] 62 -> 5, 21 +++ Blue subgraph (GB) [b] 0 -> 6 [b] 2 -> 4 [b] 4 -> 2 [b] 6 -> 0, 39 [b] 7 -> 9 [b] 9 -> 7 [b] 12 -> [b] 15 -> [b] 16 -> 27, 48, 60 [b] 17 -> [b] 18 -> [b] 23 -> [b] 27 -> 16 [b] 28 -> 47 [b] 31 -> [b] 32 -> [b] 33 -> 60 [b] 37 -> 52 [b] 39 -> 6 [b] 40 -> [b] 42 -> [b] 43 -> [b] 44 -> [b] 47 -> 28 [b] 48 -> 16 [b] 52 -> 37 [b] 53 -> [b] 55 -> [b] 57 -> 60 [b] 58 -> [b] 60 -> 16, 33, 57 [b] 63 -> +++ Red cycles +++ Blue cycles +++ Nonmonochromatic graph (GRB) [b] 0 -> 6 [r] 1 -> 33 [b] 2 -> 46, 4 [r] 3 -> 49, 46 [b] 4 -> 25, 2 [r] 5 -> 57, 62 [b] 6 -> 39, 0 [b] 7 -> 24, 9 [r] 8 -> 55 [b] 9 -> 51, 7 [r] 10 -> [r] 11 -> 57 [b] 12 -> 26 [r] 13 -> [r] 14 -> [b] 15 -> [b] 16 -> 35, 60, 48, 27 [b] 17 -> 22 [b] 18 -> [r] 19 -> 36, 49 [r] 20 -> 54 [r] 21 -> 61, 62 [r] 22 -> 53, 52, 32, 17, 45 [b] 23 -> 24 [r] 24 -> 23, 7, 35 [r] 25 -> 60, 4 [r] 26 -> 44, 43, 37, 27, 12 [b] 27 -> 59, 26, 16 [b] 28 -> 46, 47 [r] 29 -> 49 [r] 30 -> [b] 31 -> [b] 32 -> 22 [b] 33 -> 1, 60 [r] 34 -> [r] 35 -> 16, 24 [r] 36 -> 19 [b] 37 -> 26, 52 [r] 38 -> 39, 41 [b] 39 -> 49, 38, 6 [b] 40 -> [r] 41 -> 54, 38 [b] 42 -> 46, 45 [b] 43 -> 62, 26 [b] 44 -> 26 [r] 45 -> 42, 22 [r] 46 -> 42, 28, 2, 3 [b] 47 -> 28 [b] 48 -> 16 [r] 49 -> 39, 3, 29, 19 [r] 50 -> 59 [r] 51 -> 9 [b] 52 -> 22, 37 [b] 53 -> 22 [r] 54 -> 57, 20, 41 [b] 55 -> 8 [r] 56 -> 57 [b] 57 -> 61, 56, 54, 11, 5, 60 [b] 58 -> [r] 59 -> 27, 50 [b] 60 -> 25, 16, 57, 33 [r] 61 -> 57, 21 [r] 62 -> 43, 5, 21 [b] 63 -> +++ Multi-color cycles (21, 61, 57, 5, 62), Color: (r, r, b, r, r) (38, 41, 54, 57, 5, 62, 43, 26, 37, 52, 22, 45, 42, 46, 3, 49, 39), Color: (r, r, r, b, r, r, b, r, b, b, r, r, b, r, r, r, b) (2, 4, 25, 60, 57, 5, 62, 43, 26, 37, 52, 22, 45, 42, 46), Color: (b, b, r, b, b, r, r, b, r, b, b, r, r, b, r) (27, 16, 60, 57, 5, 62, 43, 26), Color: (b, b, b, b, r, r, b, r) ====================================================================================================