Exposé sur des extensions du théorème de Grötzsch
/Exposé en anglais/Talk in english/
The Grötzsch Theorem states that every triangle-free planar graph admits a proper 3-coloring. Among many of its generalizations, the one of Grünbaum and Aksenov, giving 3-colorability of planar graphs with at most three triangles, is perhaps the most known. A lot of attention was also given to extending 3-colorings of subgraphs to the whole graph. In this paper, we consider 3-colorings of planar graphs with at most one triangle. Particularly, we show that precoloring of any two non-adjacent vertices and precoloring of a face of length at most 4 can be extended to a 3-coloring of the graph. Additionally, we show that for every vertex of degree at most 3, a precoloring of its neighborhood with the same color extends to a 3-coloring of the graph. The latter result implies an affirmative answer to a conjecture on adynamic coloring. All the presented results are tight.
[Hoang La] (LIRMM)
[ https://www.tcs.uj.edu.pl/walczak | https://www.lirmm.fr/xuan-hoang-la/ ]
{Remarques/Remarks}
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N'hésitez pas à venir un peu avant le début de l'exposé pour faire des tests (et discuter informellement). Nous auront également des discussions informelles post-GT.
À très bientôt,
Claire, 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,
Claire, 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