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We show that for a large class of Artin groups with Dynkin diagrams being atree, the $K(\pi,1)$-conjecture holds. We also establish the$K(\pi,1)$-conjecture for another class of Artin groups whose Dynkin diagramscontain a cycle, which applies to some hyperbolic type Artin groups. This isbased on a new approach to the $K(\pi,1)$-conjecture for Artin groups.

Labeled four cycles and the $K(\pi,1)$-conjecture for Artin groups