Prof. Emo Welzl and Prof. Bernd Gärtner
|Mittagsseminar Talk Information|
Date and Time: Thursday, August 25, 2022, 12:15 pm
Duration: 30 minutes
Location: OAT S15/S16/S17
Speaker: Emanuel Seemann
We investigate the Hamiltonicity and matching properties of 1-planar graphs, a class of beyond planar graphs that allow for at most one crossing per edge. In 2019 Biedl generalized a known Hamiltonicity result by Tutte for planar graphs to 1-planar graphs. Biedl showed that a certain subclass of 4-connected 1-planar graphs is Hamiltonian. We prove that one can prescribe an edge to this Hamiltonian cycle. Using our result we provide sufficient conditions under which all matchings of size 1 and 2 can be extended to a perfect matching in an even 1-planar graph. This generalizes previous results by Plummer for planar graphs and Fujisawa et al. for 1-planar graphs.
The results are part of my master's thesis "Matchings and Hamiltonian cycles in 1-planar graphs" supervised by Michael Hoffmann, Meghana Mallik Reddy and Emo Welzl.
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