The Planar Cayley Graphs are Effectively Enumerable I: Consistently Planar Graphs

摘要

We show that a group admits a planar, finitely generated Cayley graph if andonly if it admits a special kind of group presentation we introduce, called aplanar presentation. Planar presentations can be recognised algorithmically. Asa consequence, we obtain an affirmative answer to a question of Droms et al.asking whether these groups can be effectively enumerated.