Solution of an Erdős Problem: The O’Donnell Theorem

In a surprising twist, the complete solution of Paul Erdős’ old July 1975 problem about unit distance 4-chromatic graphs of arbitrary girth comes out to be simpler than all partial solutions, we have discussed in the previous two chapters. In another surprise, Paul O’Donnell uses in his solution the 1966 result obtained jointly by Paul Erdős and Andras Hajnal, the result that has been known all alone, but no one noticed its connection to the problem at hand. You may wish to revisit definitions of uniform hypergraphs in the beginning of Chap. 48 .