# This file describes a set of rules equivalent to the set from the paper # `The Four-Colour Theorem' by N. Robertson, D. P. Sanders, P. D. Seymour # and R. Thomas. Please refer to the manuscript `Discharging Cartwheels'. # As explained therein, to describe a rule we list beta(v_0), delta(v_0), # beta(v_1), delta(v_1), and all triples (i,beta(v_i),delta(v_i)) such # that 2<=i<=16 and v_i belongs to V(G). # # The first line of each rule describes beta(v_0), delta(v_0), beta(v_1) # and delta(v_1) using the convention that "5" means "55", "6" means "66", # etc. The second line describes all triples (i,beta(v_i),delta(v_i)) # using the same convention as above and interpreting "9" to mean "12". # If there are no triples (i,beta(v_i),delta(v_i)), then the second line # is omitted. # # 22 April 1995, slightly revised 14 January 1997 # # # Rule 1 1 5 59 2 invert # Rule 2 3 56 79 3 5 4 invert # Rule 3 5 56 69 3 56 5 5 6 invert # Rule 4 7 6 69 3 5 5 56 9 5 8 invert 9 6 69 3 6 5 56 9 5 10 invert # Rule 5 11 6 69 3 6 5 6 9 56 11 5 12 invert # Rule 6 13 6 79 3 5 5 6 7 5 9 56 14 invert # Rule 7 15 6 79 3 6 5 6 7 5 9 6 11 56 16 invert # Rule 8 17 7 79 3 56 5 5 18 invert # Rule 9 19 7 79 3 56 5 56 14 5 20 invert # Rule 10 21 7 79 2 5 3 5 4 5 5 5 22 7 79 2 5 3 5 4 5 5 69 23 invert # Rule 11 24 7 79 2 5 3 5 4 6 5 69 8 5 25 invert # Rule 12 26 7 79 2 5 3 5 4 5 5 5 8 5 9 5 # Rule 13 27 7 89 2 5 3 5 4 6 5 5 6 5 8 5 28 invert # Rule 14 29 7 79 2 6 3 5 4 5 8 5 30 invert # Rule 15 31 7 79 2 6 3 5 4 5 5 79 12 6 13 5 32 invert # Rule 16 33 7 79 2 6 3 5 4 6 5 5 12 6 13 5 34 invert # Rule 17 35 7 79 2 6 3 5 4 5 5 5 8 6 12 5 13 79 36 invert # Rule 18 37 7 7 2 69 3 5 5 6 7 5 9 5 14 5 38 invert # Rule 19 39 7 89 2 69 3 5 4 6 5 6 7 5 9 5 12 6 13 5 40 invert # Rule 20 41 7 79 2 6 3 6 4 5 5 6 12 5 13 5 42 invert # Rule 21 43 7 7 2 6 3 69 4 56 6 5 12 5 13 5 44 invert # Rule 22 45 7 7 2 6 3 69 4 5 6 5 12 6 13 5 46 invert # Rule 23 47 7 79 2 5 3 7 5 5 9 5 48 invert # Rule 24 49 7 7 2 5 3 79 4 5 5 6 6 5 12 5 13 6 50 invert # Rule 25 51 7 79 2 5 3 7 4 5 5 5 9 6 11 5 14 5 52 invert # Rule 26 53 7 7 2 6 3 79 4 6 5 5 6 5 12 6 13 5 54 invert # Rule 27 55 7 7 2 6 3 7 4 79 5 56 6 6 9 5 15 5 16 69 56 invert # Rule 28 57 8 79 2 5 3 5 4 5 5 5 12 5 58 invert # Rule 29 59 8 79 2 5 3 5 4 5 8 5 12 5 13 5 60 invert # Rule 30 61 8 79 2 5 3 5 4 5 5 6 9 5 14 5 62 invert # Rule 31 63 8 79 2 5 3 5 4 5 5 5 8 5 9 5 12 69 14 69 64 8 79 2 5 3 5 4 5 5 5 8 5 9 69 12 69 14 69 65 invert # Rule 32 66 8 7 2 6 3 79 4 5 5 6 6 5 12 5 13 5 14 5 67 invert