The absence of efficient dual pairs of spanning trees in planar graphs.
The genera, reflexibility and simplicity of regular maps
This paper uses combinatorial group theory to help answer some long-standing questions about the genera of orientable surfaces that carry particular kinds of regular maps. By classifying all orientably-regular maps whose automorphism group has order coprime to , where is the genus, all orientably-regular maps of genus for prime are determined. As a consequence, it is shown that orientable surfaces of infinitely many genera carry no regular map that is chiral (irreflexible), and that orientable...
The neighborhood complex of an infinite graph.
The reflexible hypermaps of characteristic
Thin presentation of knots and lens spaces.
Toward optimality in discrete Morse theory.