Fig. 8

(i) Resolved component (\(\text {score}=1\)): a 6-cycle alternating (black) \(\check{\mathbb {D}}\)- and (blue) \(\mathbb {S}\)-edges, without intersections. (ii) Two 6-cycles share one \(\check{\mathbb {D}}\mathbb {S}\check{\mathbb {D}}\)-path composed of the two black \(\check{\mathbb {D}}\)-edges with the blue \(\mathbb {S}\)-edge in between. (iii) Unsaturated triplet with \(\text {score}=1\): every \(\check{\mathbb {D}}\mathbb {S}\check{\mathbb {D}}\)-path including the same \(\check{\mathbb {D}}\)-edge (the thick black one) occurs in two distinct 6-cycles. The thick black \(\check{\mathbb {D}}\)-edge occurs in four 6-cycles, all other black edges occur in two 6-cycles. (iv) Saturated triplet with \(\text {score}=2\): every \(\check{\mathbb {D}}\mathbb {S}\check{\mathbb {D}}\)-path occurs in two distinct 6-cycles, every black edge occurs in four 6-cycles