Let G be a group and π be a set of primes. We consider the set cd~π (G) of character degrees of G that are divisible only by primes in π. In particular, we define Γ~π (G) to be the graph whose vertex set is the set of primes dividing degress in cd~π (G). There is an edge between p and q if pq divides a degree a ∈ cd~π (G). We show that if G is π-solvable, then Γ~π(G) has at most two connected components.
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