Partial duality and closed 2-cell embeddings To Adrian Bondy on his 70th birthday
نویسندگان
چکیده
In 2009 Chmutov introduced the idea of partial duality for embeddings of graphs in surfaces. We discuss some alternative descriptions of partial duality, which demonstrate the symmetry between vertices and faces. One is in terms of band decompositions, and the other is in terms of the gem (graph-encoded map) representation of an embedding. We then use these to investigate when a partial dual is a closed 2-cell embedding, in which every face is bounded by a cycle in the graph. We obtain a necessary and sufficient condition for a partial dual to be closed 2-cell, and also a sufficient condition for no partial dual to be closed 2-cell.
منابع مشابه
Mathias and set theory
On the occasion of his 70th birthday, the work of Adrian Mathias in set theory is surveyed in its full range and extent.
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