/Exposé en anglais/Talk in english/
In 1974, Erdős posed the following problem. Given an oriented graph H, determine or estimate the maximum possible number of H-free orientations of an n-vertex graph. When H is a tournament, the answer was determined precisely for sufficiently large n by Alon and Yuster. In general, when the underlying undirected graph of H contains a cycle, one can obtain accurate bounds by combining an observation of Kozma and Moran with celebrated results on the number of F-free graphs. We resolve all remaining cases in an asymptotic sense, thereby giving a rather complete answer to Erdős's question. Moreover, we determine the answer exactly when H is an odd cycle and n is sufficiently large, answering a question of Araújo, Botler and Mota.
Joint work with Matija Bucic and Benny Sudakov.
[Oliver Janzer] (ETH Zürich)
https://sites.google.com/view/oliver-janzer/home
{Remarques/Remarks}
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À très bientôt,
Marthe & Jonathan
Retrouvez toutes les informations du GT dématérialisé sur https://combalgo.labri.fr/pmwiki.php/Groupe/GT-en-LIGNE
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This presentation will be recorded, please deactivate your webcam and microphone if you do not wish to appear on the recording. Informal exchanges before and after the presentation, as well as questions, will not be recorded.
Do not hesitate to come a little before the start of the presentation to test (and chat informally). We will also have informal post-working group discussions.
See you soon,
Marthe & Jonathan
Find all the information of the dematerialized working group on the web page https://combalgo.labri.fr/pmwiki.php/Groupe/GT-en-LIGNE