Polynomial χ-boundedness of grounded segment graphs

A grounded segment graph is the intersection graph of a collection of line segments grounded on a common line. Grounded segment-graph conjecture. The class of grounded segment graphs is polynomially χ-bounded. Grounded segment graphs are a class of geometric intersection graphs; the conjecture asks whether their chromatic number is bounded by a polynomial in their clique number, extending the polynomial χ-boundedness results discussed for related grounded classes. The source presents this as an open question and gives no resolution.