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Soient donn\'es deux graphes $\Gamma_1$, $\Gamma_2$ \`a $n$ sommets. Sont-ilsisomorphes? S'ils le sont, l'ensemble des isomorphismes de $\Gamma_1$ \`a$\Gamma_2$ peut \^etre identifi\'e avec une classe $H \pi$ du groupesym\'etrique sur $n$ \'el\'ements. Comment trouver $\pi$ et des g\'en\'erateursde $H$? Le d\'efi de donner un algorithme toujours efficace en r\'eponse \`aces questions est rest\'e longtemps ouvert. Babai a r\'ecemment montr\'ecomment r\'esoudre ces questions -- et d'autres qui y sont li\'ees -- en tempsquasi-polynomial, c'est-\`a-dire en temps $\exp(O(\log n)^{O(1)})$. Sastrat\'egie est bas\'ee en partie sur l'algorithme de Luks (1980/82), qui ar\'esolu le cas de graphes de degr\'e born\'e.  English translation:  Graph isomorphisms in quasipolynomial time [after Babai and Luks,Weisfeiler--Leman,...]. Let $\Gamma_1$, $\Gamma_2$ be two graphs with $n$vertices. Are they isomorphic? If any isomorphisms from $\Gamma_1$ to$\Gamma_2$ exist, they form a coset $H \pi$ in the symmetric group on $n$elements. How can we find a representative $\pi$ and a set of generators for$H$? Finding an algorithm that answers such questions efficiently (in allcases) is a challenge that has long remained open. Babai has recently shown howto solve these problems and related ones in quasipolynomial time, i.e., time$\exp(O(\log n)^{O(1)})$. His strategy is based in part on an algorithm due toLuks (1980/82), who solved the case of graphs of bounded degree.

Isomorphismes de graphes en temps quasi-polynomial (d'apr\`es Babai et Luks, Weisfeiler-Leman...)