In 2020, Naserasr, Wang and Zhu in [6] constructed a signed planar graph (G,s) that has a ?c(G) = 4 + . Moreover every planar signed graph (G,s) has a ?c(G) < 6. This paper continues to reinforce this result by using a method allowing to construct, for each rational r < 6, a signed planar graph (G,s) whose ?c(G) = r. Considering the previous findings of Moser [2] in 1997 and Zhu [17] in 2001, this clearly indicates that any rational r is the circular chromatic number of a planar signed graph.
Planar signed graphs, circular coloring, circular-r-coloring
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