Induced subgraphs of graphs with large chromatic number. I. Odd holes
  An odd hole in a graph is an induced subgraph which is a cycle of odd length at least five. In 1985, A. Gyarfas made the conjecture that for all t there exists n such that every graph with no K_t subgraph and no odd hole is n-colourable. We prove this conjecture. 
Alex Scott and Paul Seymour
math.CO