5 research outputs found
The planar Cayley graphs are effectively enumerable I: consistently planar graphs
We obtain an effective enumeration of the family of finitely generated groups
admitting a faithful, properly discontinuous action on some 2-manifold
contained in the sphere. This is achieved by introducing a type of group
presentation capturing exactly these groups.
Extending this in a companion paper, we find group presentations capturing
the planar finitely generated Cayley graphs. Thus we obtain an effective
enumeration of these Cayley graphs, yielding in particular an affirmative
answer to a question of Droms et al.Comment: To appear in Combinatorica. The second half of the previous version
is arXiv:1901.0034
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Graph Theory
This workshop focused on recent developments in graph theory. These included in particular recent breakthroughs on nowhere-zero flows in graphs, width parameters, applications of graph sparsity in algorithms, and matroid structure results