Abstract
A cycle with four blocks C(k1,k2,k3,k4) is an oriented cycle formed of four blocks of lengths k1,k2,k3 and k4 respectively. We conjecture that for every positive integers k1,k2,k3,k4, there is an integer g(k1,k2,k3,k4) such that every strongly connected digraph with chromatic number greater than g(k1,k2,k3,k4) contains a subdivision of C(k1,k2,k3,k4). As evidence, we prove this conjecture for k2=k3=k4=1.
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