n = 37  |E| = 263  w = 30  n-w = 7
degree multiset: [(29, 1), (28, 1), (27, 1), (26, 1), (25, 1), (24, 1), (23, 1), (22, 1), (21, 1), (20, 1), (19, 1), (18, 1), (17, 1), (16, 1), (15, 1), (14, 1), (13, 8), (12, 1), (11, 1), (10, 1), (9, 1), (8, 1), (7, 1), (6, 1), (5, 1), (4, 1), (3, 1), (2, 1), (1, 1), (0, 1)]
odd cycle of length 3 : [5, 0, 13]
3-colouring verified on all edges; class sizes [7, 12, 18]
chi = 3 ; ceil(floor(w/2)/(n-w)) = 3 ; Melnikov requires chi > 3 : False
(2chi-1)(n-w) = 35  vs n-1 = 36
