Construction of Kn-minor free graphs with given circular chromatic number Original Research Article

For each integer n⩾5 and each rational number r in the interval [2,n−1], we construct a Kn-minor free graph G with χc(G)=r. This answers a question asked by Zhu (Discrete Mathematics, 229 (1–3) (2001) 371). In case n=5, the constructed graphs are actually planar. Such planar graphs were first constructed in J. Graph Theory 24 (1997) 33 (for ∈[2,3]) and in J. Combin. Theory 76 (1999) 170 (for r∈[3,4]). However, our construction and proof are much simpler.