It was proved by Tait that for the 4 color theorem it is sufficient to prove that any planer graph can be line-3-colorable. Petersen( 1890) give an example to a graph which is not line-3-colorable. Isaacs fundamental paper(1975) present a infinite familly of such graphs. A prove that any un-colorable graph should contain the Petersen graph which is not planer, solved the 4CT problem.