On cyclically 4-connected cubic graphs

Figures & data

Figure 1: $Q_{2k}$, $k\ge 4$ (left), and $V_{2k}$, $k\ge 4$ (right).

Figure 2: Examples of cycle spread.

Figure 3: Bridging two edges.

Figure 4: All 3-connected cubic graphs with 6, 7, and 8 vertices.

Figure 5: All cyclically 4-connected cubic graphs with 8 and 10 vertices.

Figure 6: A pair of edges in H with cycle spread $(1,1)$ with edges be and df incident to b and d.

Figure 7: Exchanging one pair of bridged edges for another.

Figure 8: Exchanging a bridge of one edge pair with cycle spread $(1,1)$ for another (left) and a 4-cycle chain (right).

Figure 9: Exchanging bridges of pairs of edges with cycle spread $(1,1)$ in $Q_{2k}$ and $V_{2k}$ to reach the same graph.

Figure 10: Planar graphs obtained by bridging edges in $Q_{10}$.

Figure 11: Counterexamples to Lemma 3.1 if G contains triangles (left) or is not cubic (right).

Figure 12: The non-isomorphic cyclically 4-connected bridge additions of $V_{10}$.

Figure 13: The non-isomorphic cyclically 4-connected bridge additions of $P_{10}$.