The fractional version of Hedetniemi’s conjecture is true

This paper proves that the fractional version of Hedetniemi’s conjecture is true. Namely, for any graphs G and H , χ f ( G × H ) = min { χ f ( G ) , χ f ( H ) } . As a by-product, we obtain a proof of the Burr–Erdős–Lovász conjecture: For any positive integer n , there exists an n -chromatic graph G whose chromatic Ramsey number equals ( n − 1 ) 2 + 1 .