An analogue of Hajós’ Theorem for the circular chromatic number

Source abstract

This paper designs a set of graph operations and proves that starting from G d k G^k_d , by repeatedly applying these operations, one can construct all graphs G G with χ c ( G ) ≥ k / d \chi _c(G) \geq k/d (for k / d ≥ 3 k/d \geq 3 ). This can be viewed as an analogue of Hajós’ Theorem for the circular chromatic number.