Comportement à l'infini du graphe gordien des nœuds

We study the Gordian graph of all knots in R3: two knots are adjacent if they differ by a single crossing change. We prove that this graph contains isometrically an infinite countable tree with infinite valency, and that the complement of any finite subset is connected. To cite this article: J. Marché, C. R. Acad. Sci. Paris, Ser. I 340 (2005).