Cyclically five-connected cubic graphs

  title={Cyclically five-connected cubic graphs},
  author={Neil Robertson and Paul D. Seymour and Robin Thomas},
  journal={J. Comb. Theory, Ser. B},
A cubic graph G is cyclically 5-connected if G is simple, 3–connected, has at least 10 vertices and for every set F of edges of size at most four, at most one component of G\F contains circuits. We prove that if G and H are cyclically 5-connected cubic graphs and H topologically contains G, then either G and H are isomorphic, or (modulo well-described exceptions) there exists a cyclically 5-connected cubic graph G such that H topologically contains G and G is obtained from G in one of the… CONTINUE READING
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