Let G be a finite group and let cd(G) be the set of all complex irreducible character degrees of G. Let ?(G) be the set of primes that divide degrees in cd(G). The prime graph ?(G) has vertex set ?(G) and there is an edge between two distinct vertices p and q if pq divides some degrees a ? cd(G). A fundamental result by P.P. P?lfy asserts that the complement¯?(G) of the graph ?(G) does not contain any cycle of length ?. We generalize P?lfy’s result, showing that ¯?(G) does not contain any cycle of odd length, whence it is a bipartite graph.
