Formulation of the Kneser Conjecture

Considering the elementary definition of the Kneser graphs, it turned out to be surprisingly difHcult to determine their chromatic numbers. 

The Kneser conjecture states that in fact equality holds. This was proved in 1978 by L. Lovasz, who used geometric obstructions of Borsuk-Ulam type to show the nonexistence of certain graph colorings. 

Theorem 17.21 was rather influential for further developments in this field. We shall sketch the modern version of its proof in the next three subsections. 

---