The planar Cayley graphs are e↵ectively enumerable
نویسندگان
چکیده
We show that a group admits a planar, finitely generated Cayley graph if and only if it admits a special kind of group presentation we introduce, called a planar presentation. Planar presentations can be recognised algorithmically. As a consequence, we obtain an e↵ective enumeration of the planar Cayley graphs, yielding in particular an a rmative answer to a question of Droms et al. asking whether the planar groups can be e↵ectively enumerated.
منابع مشابه
The planar Cayley graphs are effectively enumerable
We show that a group admits a planar, finitely generated Cayley graph if and only if it admits a special kind of group presentation we introduce, called a planar presentation. Planar presentations can be recognised algorithmically. As a consequence, we obtain an effective enumeration of the planar Cayley graphs, yielding in particular an affirmative answer to a question of Droms et al. asking w...
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