The boxicity of a finite simple graph 
is the least nonnegative integer 
for which 
is the intersection graph
of axis-parallel closed boxes in 
. A box is a Cartesian
product of 
closed intervals. By convention, complete
graphs have boxicity zero (Chandran et al. 2026).
Equivalently, boxicity is the least number of interval graphs on the same vertex set whose edge
sets have intersection 
. Each coordinate of a box
representation supplies an interval graph, and
taking their common edges recovers 
(Chandran et al. 2026). In particular, noncomplete
interval graphs have boxicity 1.
For Kneser graphs 
with 
and 
, Chandran and Sahoo
(2026) proved the lower bound 
.
