Let G be a graph and W be a set of some subgraphs of G.An m-edge-coloring of G is called W-polychromatic if every subgraph isomorphic to some element from W receives all m colors.In this paper,the close relationship between the subgraph polychromatic edge-coloring problem of graphs and the Turán problem is uncovered,and the W-polychromatic edge-coloring problem of the complete bipartite graph Kn,n is studied.We determine the exact value of the W-polychomatic number to be n+1,n+1,(∟)n2/3」,respectively,when W is one of three sets of subgraphs of Kn,n:Hamilton cycles,2-factors,Kn-1,n-1's.Furthermore,when the host graph is Kn,n,we show that the Turan number of any 2-factor of Kn,n is n2-n+1.
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