graph theory In mathematics, graph theory is the study of ''graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of '' vertices'' (also called ''nodes'' or ''points'') which are conne ...

, a b-coloring of a

graph Graph may refer to: Mathematics *Graph (discrete mathematics), a structure made of vertices and edges **Graph theory, the study of such graphs and their properties *Graph (topology), a topological space resembling a graph in the sense of discre ...

is a coloring of the vertices where each color class contains a vertex that has a neighbor in all other color classes. The b-chromatic number of a ''G'' graph is the largest b(G) positive integer that the ''G'' graph has a b-coloring with b(G) number of colors. Victor Campos, Carlos Lima és Ana SilvaV. Campos, C. Lima, A. Silva: "b-coloring graphs with girth at least 8." The Seventh European Conference on Combinatorics, Graph Theory and Applications. Scuola Normale Superiore (2013). used the relation between b-coloring and a graph's smallest cycle to partly prove the

Erdős–Faber–Lovász conjecture In graph theory, the Erdős–Faber–Lovász conjecture is a problem about graph coloring, named after Paul Erdős, Vance Faber, and László Lovász, who formulated it in 1972.. It says: :If complete graphs, each having exactly vertices, have ...

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Graph coloring