On Polyhedral Embeddings of Cubic Graphs
Bojan Mohar, Andrej Vodopivec · Combinatorics Probability Computing · 2006
Polyhedral embeddings of cubic graphs by means of certain operations are studied. It is proved that some known families of snarks have no (orientable) polyhedral embeddings. This result supports a conjecture of Grünbaum that no snark admits an orientable polyhedral embedding. This conjecture is verified by computer for all snarks having fewer than 30 vertices. On the other hand, for every non-orientable surface .