No 6-regular 4-vertex-critical graphs on n≤15 except one on 13 vertices; every 6-edge-cut in a 6-regular (4,1)-graph is a vertex star or has shores ≥15, with no bipartite shores on nontrivial cuts.
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Exact 6-cut rigidity and small-order superconnectivity for the 6-regular case of Dirac's k=4 problem
No 6-regular 4-vertex-critical graphs on n≤15 except one on 13 vertices; every 6-edge-cut in a 6-regular (4,1)-graph is a vertex star or has shores ≥15, with no bipartite shores on nontrivial cuts.