The zero-sum Ramsey number 
of a finite simple
graph 
, for an integer 
dividing its edge count,
is the least positive integer 
such that every labeling of the edges
of the complete graph 
by elements of 
contains a copy of 
whose graph edge labels sum
to zero in 
(Bialostocki and Dierker 1994, Wang and Wang 2026). Here 
is the additive cyclic group
of residues modulo 
. The copy need not be an induced
subgraph. This replaces the monochromatic-copy condition in an ordinary Ramsey
number by a congruence condition on the sum of
the labels.
Wang and Wang (2026) constructed trees 
, for every positive
integer 
, with 
edges such that
 |
where 
is the ordinary two-color Ramsey number. The tree 
is obtained from a star graph
with 
leaves by subdividing 
distinct edges once. Consequently,
the ratio 
has limit
inferior at least 
. This refutes the
uniform asymptotic ratio 1 conjectured by Bialostocki and Dierker (1990) for forests
as their edge count tends to infinity.
