On Polyhedral Embeddings of Cubic Graphs
نویسندگان
چکیده
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 for all snarks having up to 30 vertices using computer. On the other hand, for every nonorientable surface S, there exists a non 3-edge-colorable graph, which polyhedrally embeds in S.
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ورودعنوان ژورنال:
- Combinatorics, Probability & Computing
دوره 15 شماره
صفحات -
تاریخ انتشار 2006