Circular Coloring Signed Graphs Has No Contains Kk minor
In 1943, Hugo Hadwiger showed that any graph that contains no K4 minors is 3colorable. He considers any graph which has no Kk 1 minors is k colorable. Based on Naserasr, Wang and Zhu’s definitions of the circular chromatic number for a signed graph, particular generalized versions of Hadwiger’s conjecture that might be valid in a class of sign graphs are formalized. We prove in this paper that, if the signed graph G s has no Kk 1, minor, it means that c G s = 3.
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