28 research outputs found
The chromatic number of almost stable Kneser hypergraphs
Let be the set of -subsets of such that for all
, we have We define almost -stable Kneser hypergraph
to be the
-uniform hypergraph whose vertex set is and whose edges are the
-uples of disjoint elements of .
With the help of a -Tucker lemma, we prove that, for prime and for
any , the chromatic number of almost 2-stable Kneser hypergraphs
is equal
to the chromatic number of the usual Kneser hypergraphs ,
namely that it is equal to
Defining to be the number of prime divisors of , counted with
multiplicities, this result implies that the chromatic number of almost
-stable Kneser hypergraphs is equal to the
chromatic number of the usual Kneser hypergraphs for any
, namely that it is equal to $\lceil\frac{n-(k-1)r}{r-1}\rceil.
Choice number of Kneser graphs
In this short note, we show that for any and
the choice number of the Kneser graph is