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The b-chromatic number of cubic graphs [Elektronski vir]
Klavžar, Sandi ; Jakovac, Marko
The ▫$b$▫-chromatic number of a graph ▫$G$▫ is the largest integer ▫$k$▫ such that ▫$G$▫ admits a proper ▫$k$▫-coloring in which every color class contains at least one vertex adjacent to some vertex ...in all the other color classes. It is proved that with four exceptions, the b-chromatic number of cubic graphs is 4. The exceptions are the Petersen graph, ▫$K_{3,3}$▫, the prism over ▫$K_3$▫, andone more sporadic example on 10 vertices.
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