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We prove a new inequality for the asymptotic dimension of HNN-extensions. Wededuce that the asymptotic dimension of every finitely generated one relatorgroup is at most two, confirming a conjecture of A.Dranishnikov. As furthercorollaries we calculate the exact asymptotic dimension of Right-angled Artingroups and we give a new upper bound for the asymptotic dimension offundamental groups of graphs of groups.

Asymptotic Dimension of Graphs of Groups and One Relator Groups