The b-chromatic index of a graph
نویسندگان
چکیده
The b-chromatic index φ(G) of a graph G is the largest integer k such that G admits a proper k-edge coloring in which every color class contains at least one edge incident to some edge in all the other color classes. The b-chromatic index of trees is determined and equals either to a natural upper bound m(T ) or one less, where m(T ) is connected with the number of edges of high degree. Some conditions are given for which graphs have the b-chromatic index strictly less than m(G), and for which conditions it is exactly m(G). In the last part of the paper regular graphs are considered. It is proved that with four exceptions, the b-chromatic number of cubic graphs is 5. The exceptions are K4, K3,3, the prism over K3, and the cube Q3.
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