For a finite group G, we write cρ(G) to denote the prime divisor set of the various conjugacy class lengths of G and cσ(G) the maximum number of distinct prime divisors of a single conjugacy class length of G. It is a famous open problem that |cρ(G)| can be bounded by cσ(G). Let G be an almost simple group G such that the graph Γ(G) built on element orders is a tree. By using Lucido's classification theorem, we prove |cρ(G)| = cσ(G) except possibly when G is isomorphic to PSL_2(p~f)<α>, where p is an odd prime and α is a field automorphism of odd prime order f. In the exceptional case, |cρ(G)| ≤ cσ(G) + 2. Combining with our known result, we also prove that for a finite group G with Γ(G) a forest, the inequality |cρG| ≤ 2cσ(G) is true.
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