1 research outputs found
Chromatic-choosability of hypergraphs with high chromatic number
It was conjectured by Ohba and confirmed recently by Noel et al. that, for
any graph , if then . This
indicates that the graphs with high chromatic number are chromatic-choosable.
We show that this is also the case for uniform hypergraphs and further propose
a generalized version of Ohba's conjecture: for any -uniform hypergraph
with , if then . We show
that the condition of the proposed conjecture is sharp by giving two classes of
-uniform hypergraphs with and .
To support the conjecture, we give two classes of -uniform hypergraphs
with and prove that .Comment: 18 page