Algebraic Graph Theory Seminar - Clement Legrand (24.5.2024)

Friday 24.5.2024 at 13:00, Lecture room M/IX (online too)

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Clement Legrand (University of Bordeaux):
The structure of quasi-transitive graphs avoiding a minor

Abstract:
An infinite graph is quasi-transitive if its vertex set has finitely many orbits under the action of its automorphism group. With Louis Esperet and Ugo Giocanti, we obtain a structure theorem for locally finite quasi-transitive graphs avoiding a minor, which is reminiscent of the Robertson-Seymour Graph Minor Structure Theorem. As applications of this result, we prove that every locally finite quasi-transitive graph attains its Hadwiger number, that is, if such a graph contains arbitrarily large clique minors, then it contains an infinite clique minor. This answers a question of Thomassen from 1992. We also derive some results on the accessibility of quasi-transitive graphs and groups avoiding a minor.
Finally, we prove the minor-excluded case of a conjecture of Ballier and Stein (2018) on the domino problem.

Those of you who are not able to attend in person or who are still uncertain about the safety of attending in person are welcome to attend via MS Teams. In either case, we hope to see as many of you as possible (either in person or virtually) at our Friday gatherings.

 

 

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