A hypergraph edge coloring assigns colors to the hyperedges of a hypergraph so that intersecting hyperedges have different colors. The least number of
colors in such a coloring is its chromatic index 
. Repeated hyperedges
are allowed when 
is a multihypergraph. The degree of a graph
vertex is the number of incident hyperedges, counted
with multiplicity, and 
is the maximum of these degrees.
Alon and Kim (1997) conjectured the following asymptotic bound. For fixed integers 
and every 
, a 
-uniform multihypergraph in which distinct hyperedges
intersect in at most 
vertices satisfies
 |
when 
is sufficiently large, with its threshold depending on 
, 
,
and 
. Here 
-uniform means that each hyperedge
has exactly 
vertices. Qiao et al. (2026) report a proof
of this bound. For a linear hypergraph, the
intersection condition holds with 
,
giving an asymptotic coefficient 1.
