We are delighted to announce that the ePCC <https://pcc2020.github.io/> (postgraduate combinatorics online seminar series) will run its first virtual seminar on Wednesday November 11th at 1530; the speaker will be Deniz Sarikaya <http://www.denizsarikaya.de/>.
The details of the first talk follow.
Speaker: Deniz Sarikaya <http://www.denizsarikaya.de/>
Title of the talk: A primer to topological infinite graph theory and how to force Hamiltonicity in locally finite graphs via forbidden induced subgraphs
Abstract:
The study of Hamiltonian graphs, i.e. graphs having a cycle that contains all vertices of the graph, is a central theme of finite graph theory. For infinite graphs such a definition cannot work, since cycles are finite. We shall debate possible concepts of Hamiltonicity for infinite graphs and eventually follow the topological approach by Diestel and Kühn [1,2], which allows to generalize several results about being a Hamiltonian graph to locally finite graphs, i.e. graphs where each vertex has finite degree. An infinite cycle of a locally finite connected graph G is defined as a homeomorphic image of the unit circle S^1 in the Freudenthal compactification |G| of G. Now we call G Hamiltonian if there is an infinite cycle in |G| containing all vertices of G. We examine how to force Hamiltonicity via forbidden induced subgraphs and present recent extensions of results for Hamiltonicity in finite claw-free graphs to locally finite ones. This is joint work with Karl Heuer.
The talk is based on these papers: https://arxiv.org/abs/2006.09160 <https://arxiv.org/abs/2006.09160>, https://arxiv.org/abs/2006.09166 <https://arxiv.org/abs/2006.09166>
Bibliography [1] R. Diestel and D. Kühn, On infinite cycles I, Combinatorica 24 (2004), pp. 69-89.
[2] R. Diestel and D. Kühn, On infinite cycles II, Combinatorica 24 (2004), pp. 91-116.
To join the seminar, please use the following details:
— Join Zoom Meeting: https://uofglasgow.zoom.us/j/98659323517?pwd=U3dId0Y5SEw5b2NFQ3VEQnBYVDZnQT09 <https://uofglasgow.zoom.us/j/98659323517?pwd=U3dId0Y5SEw5b2NFQ3VEQnBYVDZnQT09>
— Meeting ID: 986 5932 3517
— Passcode: clique
We will be announcing future talks only through the mailing list, so sign up here <https://docs.google.com/forms/d/e/1FAIpQLSdSbI4uNwyJ_0XqoBbNV5WDsFn6W4vfOdh5qTauLrmrcNMl6Q/viewform>, if you have not already done so!
Finally, we would like to welcome you to share a talk at the ePCC. We are looking for early-career researchers who could share a talk in the second half of December or in the new year, so please get in touch with any one of the organisers!
The ePCC team.
Benjamin Merlin Bumpus <https://www.bmbumpus.com/>
Michael McKay <https://mckay2.github.io/>
Jake Horsfield <https://jakehorsfield.github.io/>
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