A box intersection graph is an intersection graph of axis-parallel boxes in Euclidean space. Each box is a Cartesian product of closed intervals, and two distinct vertices are adjacent exactly when their boxes intersect. In one dimension, these are the interval graphs.
Tomon (2026) constructed triangle-free graphs of this type in 
with arbitrarily large chromatic number. More
precisely, for infinitely many 
, there is such a graph 
on 
vertices whose independence
number satisfies
 |
and hence whose chromatic number satisfies
 |
Tomon (2026) reports that a construction was found by ChatGPT Astra under the author's guidance.
