Signed planar graphs with given circular chromatic numbers

Disproving a conjecture of Macajova, Raspaud and Skoviera, Kardos and Narboni constructed a non-4-colourable simple signed planar graph, or equivalently, a simple signed planar graph with circular chromatic number greater than 4. Naserasr, Wang, and Zhu improved this result by constructing a simple signed planar graph with circular chromatic number 14/3. This paper further strengthens this result by constructing, for each rational 4 < p/q <= 14/3, a simple signed planar graph with circular chromatic number p/q. Together with some earlier results of Moser and Zhu, this implies that every rational p/q is an element of [2, 14/3] is the circular chromatic number of a simple signed planar graph. (C) 2022 Elsevier B.V. All rights reserved.