Separating Polynomial χ -Boundedness from χ -Boundedness

Extending the idea from the recent paper by Carbonero, Hompe, Moore, and Spirkl, for every function f:ℕ→ℕ∪{∞} with f(1)=1 and f(n)⩾( [ 3n+1; 3 ]) , we construct a hereditary class of graphs 𝒢 such that the maximum chromatic number of a graph in 𝒢 with clique number n is equal to f ( n ) for every n∈ℕ . In particular, we prove that there exist hereditary classes of graphs that are χ -bounded but not polynomially χ -bounded.