Algebraic Graph Theory Seminar - Peter Zeman (13.12.2019)

Friday 13.12.2019 at 13:30, Lecture room XI

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Peter Zeman (Charles University Prague):
Automorphisms of maps in linear time

Abstract:
By a map we mean a 2-cell decomposition of a closed compact surface, i.e., an embedding of a graph such that every face is homeomorphic to an open disc. Automorphism of a map can be thought of as a permutation of the vertices which preserves the vertex-edge-face incidences in the embedding. When the underlying surface is orientable, then every automorphism of a map determines an angle-preserving homeomorphism of the surface. We present a linear-time algorithm computing the generators of the automorphism group of a map, parametrized by the genus of the underlying surface. The algorithm applies a sequence of local reductions and produces a uniform map, while preserving the automorphism group. The automorphism group of the original map can be reconstructed from the automorphism group of the uniform map in linear time. We also extend the algorithm to non-orientable surfaces by making use of the antipodal double-cover.

(Joint work with: Ken-ichi Kawarabayashi, Bojan Mohar, Roman Nedela)

 

 

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