Seminar of Graph Theory - Peter Zeman (8.4.2021)
Thursday 8.4.2021 at 9:50
By: Martin Škoviera
Peter Zeman (Charles University, Prague)>:
Jordan-like characterization of automorphism groups of planar graphs and its subclasses
MS TEAMS code (users from Comenius University in Bratislava): gglxxc7
Link (guests outside Comenius University in Bratislava)
We investigate automorphism groups of planar graphs. The main result is a complete recursive description of all abstract groups that can be realized as automorphism groups of planar graphs. The characterization is formulated in terms of inhomogeneous wreath products. In the proof, we combine techniques from combinatorics, group theory, and geometry. This significantly improves the Babai's description (1975).
In this talk we present a brief overview of the classical results and explain the method, that allowed us to solve larger problems than traditional parallelization would allow. We have successfully used cyclic graph decompositions when solving systems with millions of variables.